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Derivative of:
Derivative of (x+3)^2*(x+5)-1
Derivative of e^x/(e^x+1)
Derivative of e^(x-1)
Derivative of cos(x)-1
Identical expressions
seven *sqrt(cos(five *x)^(three))*log seven (tg(x))-(((sin(x^ two + three))^ zero . two)/tg(7^x))
7 multiply by square root of ( co sinus of e of (5 multiply by x) to the power of (3)) multiply by logarithm of 7(tg(x)) minus ((( sinus of (x squared plus 3)) to the power of 0.2) divide by tg(7 to the power of x))
seven multiply by square root of ( co sinus of e of (five multiply by x) to the power of (three)) multiply by logarithm of seven (tg(x)) minus ((( sinus of (x to the power of two plus three)) to the power of zero . two) divide by tg(7 to the power of x))
7*√(cos(5*x)^(3))*log7(tg(x))-(((sin(x^2+3))^0.2)/tg(7^x))
7*sqrt(cos(5*x)(3))*log7(tg(x))-(((sin(x2+3))0.2)/tg(7x))
7*sqrtcos5*x3*log7tgx-sinx2+30.2/tg7x
7*sqrt(cos(5*x)^(3))*log7(tg(x))-(((sin(x²+3))^0.2)/tg(7^x))
7*sqrt(cos(5*x) to the power of (3))*log7(tg(x))-(((sin(x to the power of 2+3)) to the power of 0.2)/tg(7 to the power of x))
7sqrt(cos(5x)^(3))log7(tg(x))-(((sin(x^2+3))^0.2)/tg(7^x))
7sqrt(cos(5x)(3))log7(tg(x))-(((sin(x2+3))0.2)/tg(7x))
7sqrtcos5x3log7tgx-sinx2+30.2/tg7x
7sqrtcos5x^3log7tgx-sinx^2+3^0.2/tg7^x
7*sqrt(cos(5*x)^(3))*log7(tg(x))-(((sin(x^2+3))^0.2) divide by tg(7^x))
Similar expressions
7*sqrt(cos(5*x)^(3))*log7(tg(x))-(((sin(x^2-3))^0.2)/tg(7^x))
7*sqrt(cos(5*x)^(3))*log7(tg(x))+(((sin(x^2+3))^0.2)/tg(7^x))

The derivative of the function/ 7*sqrt(cos(5*x)^(3))*log7(tg(x))-(((sin(x^2+3))^0.2)/tg(7^x))

Derivative of 7sqrt(cos(5x)^(3))*log7(tg(x))-(((sin(x^2+3))^0.2)/tg(7^x))

The solution

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                                  _____________
     ___________               5 /    / 2    \ 
    /    3       log(tan(x))   \/  sin\x  + 3/ 
7*\/  cos (5*x) *----------- - ----------------
                    log(7)            / x\     
                                   tan\7 /

$$\frac{\log{\left(\tan{\left(x \right)} \right)}}{\log{\left(7 \right)}} 7 \sqrt{\cos^{3}{\left(5 x \right)}} - \frac{\sqrt[5]{\sin{\left(x^{2} + 3 \right)}}}{\tan{\left(7^{x} \right)}}$$

(7*sqrt(cos(5*x)^3))*(log(tan(x))/log(7)) - sin(x^2 + 3)^(1/5)/tan(7^x)

Detail solution

Differentiate $\frac{\log{\left(\tan{\left(x \right)} \right)}}{\log{\left(7 \right)}} 7 \sqrt{\cos^{3}{\left(5 x \right)}} - \frac{\sqrt[5]{\sin{\left(x^{2} + 3 \right)}}}{\tan{\left(7^{x} \right)}}$ term by term:
1. Apply the quotient rule, which is:
  
  $\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$
  
  $f{\left(x \right)} = 7 \sqrt{\cos^{3}{\left(5 x \right)}} \log{\left(\tan{\left(x \right)} \right)}$ and $g{\left(x \right)} = \log{\left(7 \right)}$ .
  
  To find $\frac{d}{d x} f{\left(x \right)}$ :
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the product rule:
      
      $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
      
      $f{\left(x \right)} = \sqrt{\cos^{3}{\left(5 x \right)}}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
      1. Let $u = \cos^{3}{\left(5 x \right)}$ .
      2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
      3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \cos^{3}{\left(5 x \right)}$ :
        
        Let $u = \cos{\left(5 x \right)}$ .
        
        Apply the power rule: $u^{3}$ goes to $3 u^{2}$
        
        Then, apply the chain rule. Multiply by $\frac{d}{d x} \cos{\left(5 x \right)}$ :
        
        Let $u = 5 x$ .
        
        The derivative of cosine is negative sine:
        
        $\frac{d}{d u} \cos{\left(u \right)} = - \sin{\left(u \right)}$
        
        Then, apply the chain rule. Multiply by $\frac{d}{d x} 5 x$ :
        
        The derivative of a constant times a function is the constant times the derivative of the function.
        
        Apply the power rule: $x$ goes to $1$
        
        So, the result is: $5$
        
        The result of the chain rule is:
        
        $- 5 \sin{\left(5 x \right)}$
        
        The result of the chain rule is:
        
        $- 15 \sin{\left(5 x \right)} \cos^{2}{\left(5 x \right)}$
        
        The result of the chain rule is:
        
        $- \frac{15 \sin{\left(5 x \right)} \cos^{2}{\left(5 x \right)}}{2 \sqrt{\cos^{3}{\left(5 x \right)}}}$
      $g{\left(x \right)} = \log{\left(\tan{\left(x \right)} \right)}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
      1. Let $u = \tan{\left(x \right)}$ .
      2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
      3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \tan{\left(x \right)}$ :
        
        Rewrite the function to be differentiated:
        
        $\tan{\left(x \right)} = \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}$
        
        Apply the quotient rule, which is:
        
        $\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$
        
        $f{\left(x \right)} = \sin{\left(x \right)}$ and $g{\left(x \right)} = \cos{\left(x \right)}$ .
        
        To find $\frac{d}{d x} f{\left(x \right)}$ :
        
        The derivative of sine is cosine:
        
        $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
        
        To find $\frac{d}{d x} g{\left(x \right)}$ :
        
        The derivative of cosine is negative sine:
        
        $\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$
        
        Now plug in to the quotient rule:
        
        $\frac{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}}$
        
        The result of the chain rule is:
        
        $\frac{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)} \tan{\left(x \right)}}$
      The result is: $\frac{\left(\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right) \sqrt{\cos^{3}{\left(5 x \right)}}}{\cos^{2}{\left(x \right)} \tan{\left(x \right)}} - \frac{15 \log{\left(\tan{\left(x \right)} \right)} \sin{\left(5 x \right)} \cos^{2}{\left(5 x \right)}}{2 \sqrt{\cos^{3}{\left(5 x \right)}}}$
    So, the result is: $\frac{7 \left(\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right) \sqrt{\cos^{3}{\left(5 x \right)}}}{\cos^{2}{\left(x \right)} \tan{\left(x \right)}} - \frac{105 \log{\left(\tan{\left(x \right)} \right)} \sin{\left(5 x \right)} \cos^{2}{\left(5 x \right)}}{2 \sqrt{\cos^{3}{\left(5 x \right)}}}$
  To find $\frac{d}{d x} g{\left(x \right)}$ :
  1. The derivative of the constant $\log{\left(7 \right)}$ is zero.
  Now plug in to the quotient rule:
  
  $\frac{\frac{7 \left(\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right) \sqrt{\cos^{3}{\left(5 x \right)}}}{\cos^{2}{\left(x \right)} \tan{\left(x \right)}} - \frac{105 \log{\left(\tan{\left(x \right)} \right)} \sin{\left(5 x \right)} \cos^{2}{\left(5 x \right)}}{2 \sqrt{\cos^{3}{\left(5 x \right)}}}}{\log{\left(7 \right)}}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the quotient rule, which is:
    
    $\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$
    
    $f{\left(x \right)} = \sqrt[5]{\sin{\left(x^{2} + 3 \right)}}$ and $g{\left(x \right)} = \tan{\left(7^{x} \right)}$ .
    
    To find $\frac{d}{d x} f{\left(x \right)}$ :
    1. Let $u = \sin{\left(x^{2} + 3 \right)}$ .
    2. Apply the power rule: $\sqrt[5]{u}$ goes to $\frac{1}{5 u^{\frac{4}{5}}}$
    3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \sin{\left(x^{2} + 3 \right)}$ :
      1. Let $u = x^{2} + 3$ .
      2. The derivative of sine is cosine:
        
        $\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}$
      3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{2} + 3\right)$ :
        
        Differentiate $x^{2} + 3$ term by term:
        
        Apply the power rule: $x^{2}$ goes to $2 x$
        
        The derivative of the constant $3$ is zero.
        
        The result is: $2 x$
        
        The result of the chain rule is:
        
        $2 x \cos{\left(x^{2} + 3 \right)}$
      The result of the chain rule is:
      
      $\frac{2 x \cos{\left(x^{2} + 3 \right)}}{5 \sin^{\frac{4}{5}}{\left(x^{2} + 3 \right)}}$
    To find $\frac{d}{d x} g{\left(x \right)}$ :
    1. Let $u = 7^{x}$ .
    2. $\frac{d}{d u} \tan{\left(u \right)} = \frac{1}{\cos^{2}{\left(u \right)}}$
    3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 7^{x}$ :
      1. $\frac{d}{d x} 7^{x} = 7^{x} \log{\left(7 \right)}$
      The result of the chain rule is:
      
      $\frac{7^{x} \log{\left(7 \right)}}{\cos^{2}{\left(7^{x} \right)}}$
    Now plug in to the quotient rule:
    
    $\frac{\frac{2 x \cos{\left(x^{2} + 3 \right)} \tan{\left(7^{x} \right)}}{5 \sin^{\frac{4}{5}}{\left(x^{2} + 3 \right)}} - \frac{\left(7^{x} \log{\left(7 \right)} \sin^{2}{\left(7^{x} \right)} + 7^{x} \log{\left(7 \right)} \cos^{2}{\left(7^{x} \right)}\right) \sqrt[5]{\sin{\left(x^{2} + 3 \right)}}}{\cos^{2}{\left(7^{x} \right)}}}{\tan^{2}{\left(7^{x} \right)}}$
  So, the result is: $- \frac{\frac{2 x \cos{\left(x^{2} + 3 \right)} \tan{\left(7^{x} \right)}}{5 \sin^{\frac{4}{5}}{\left(x^{2} + 3 \right)}} - \frac{\left(7^{x} \log{\left(7 \right)} \sin^{2}{\left(7^{x} \right)} + 7^{x} \log{\left(7 \right)} \cos^{2}{\left(7^{x} \right)}\right) \sqrt[5]{\sin{\left(x^{2} + 3 \right)}}}{\cos^{2}{\left(7^{x} \right)}}}{\tan^{2}{\left(7^{x} \right)}}$
The result is: $- \frac{\frac{2 x \cos{\left(x^{2} + 3 \right)} \tan{\left(7^{x} \right)}}{5 \sin^{\frac{4}{5}}{\left(x^{2} + 3 \right)}} - \frac{\left(7^{x} \log{\left(7 \right)} \sin^{2}{\left(7^{x} \right)} + 7^{x} \log{\left(7 \right)} \cos^{2}{\left(7^{x} \right)}\right) \sqrt[5]{\sin{\left(x^{2} + 3 \right)}}}{\cos^{2}{\left(7^{x} \right)}}}{\tan^{2}{\left(7^{x} \right)}} + \frac{\frac{7 \left(\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right) \sqrt{\cos^{3}{\left(5 x \right)}}}{\cos^{2}{\left(x \right)} \tan{\left(x \right)}} - \frac{105 \log{\left(\tan{\left(x \right)} \right)} \sin{\left(5 x \right)} \cos^{2}{\left(5 x \right)}}{2 \sqrt{\cos^{3}{\left(5 x \right)}}}}{\log{\left(7 \right)}}$
Now simplify:

$\frac{\frac{35 \left(- 15 \left(\cos{\left(3 x \right)} - \cos{\left(7 x \right)}\right) \log{\left(\tan{\left(x \right)} \right)} + 8 \cos{\left(5 x \right)}\right) \sin^{\frac{4}{5}}{\left(x^{2} + 3 \right)} \cos^{2}{\left(7^{x} \right)} \cos^{2}{\left(5 x \right)} \tan^{2}{\left(7^{x} \right)}}{4} + \left(10 \cdot 7^{x} \log{\left(7 \right)} \sin{\left(x^{2} + 3 \right)} - x \left(- \sin{\left(- 2 \cdot 7^{x} + x^{2} + 3 \right)} + \sin{\left(2 \cdot 7^{x} + x^{2} + 3 \right)}\right)\right) \sqrt{\cos^{3}{\left(5 x \right)}} \log{\left(7 \right)} \cos^{2}{\left(x \right)} \tan{\left(x \right)}}{10 \sqrt{\cos^{3}{\left(5 x \right)}} \log{\left(7 \right)} \sin^{\frac{4}{5}}{\left(x^{2} + 3 \right)} \cos^{2}{\left(7^{x} \right)} \cos^{2}{\left(x \right)} \tan^{2}{\left(7^{x} \right)} \tan{\left(x \right)}}$

The answer is:

$\frac{\frac{35 \left(- 15 \left(\cos{\left(3 x \right)} - \cos{\left(7 x \right)}\right) \log{\left(\tan{\left(x \right)} \right)} + 8 \cos{\left(5 x \right)}\right) \sin^{\frac{4}{5}}{\left(x^{2} + 3 \right)} \cos^{2}{\left(7^{x} \right)} \cos^{2}{\left(5 x \right)} \tan^{2}{\left(7^{x} \right)}}{4} + \left(10 \cdot 7^{x} \log{\left(7 \right)} \sin{\left(x^{2} + 3 \right)} - x \left(- \sin{\left(- 2 \cdot 7^{x} + x^{2} + 3 \right)} + \sin{\left(2 \cdot 7^{x} + x^{2} + 3 \right)}\right)\right) \sqrt{\cos^{3}{\left(5 x \right)}} \log{\left(7 \right)} \cos^{2}{\left(x \right)} \tan{\left(x \right)}}{10 \sqrt{\cos^{3}{\left(5 x \right)}} \log{\left(7 \right)} \sin^{\frac{4}{5}}{\left(x^{2} + 3 \right)} \cos^{2}{\left(7^{x} \right)} \cos^{2}{\left(x \right)} \tan^{2}{\left(7^{x} \right)} \tan{\left(x \right)}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     ___________                                                  _____________                                ___________                     
    /    3       /       2   \              / 2    \         x 5 /    / 2    \  /       2/ x\\                /    3                           
7*\/  cos (5*x) *\1 + tan (x)/       2*x*cos\x  + 3/        7 *\/  sin\x  + 3/ *\1 + tan \7 //*log(7)   105*\/  cos (5*x) *log(tan(x))*sin(5*x)
------------------------------ - ------------------------ + ----------------------------------------- - ---------------------------------------
        log(7)*tan(x)                 4/5/ 2    \    / x\                       2/ x\                              2*cos(5*x)*log(7)           
                                 5*sin   \x  + 3/*tan\7 /                    tan \7 /

$$\frac{7^{x} \left(\tan^{2}{\left(7^{x} \right)} + 1\right) \log{\left(7 \right)} \sqrt[5]{\sin{\left(x^{2} + 3 \right)}}}{\tan^{2}{\left(7^{x} \right)}} - \frac{2 x \cos{\left(x^{2} + 3 \right)}}{5 \sin^{\frac{4}{5}}{\left(x^{2} + 3 \right)} \tan{\left(7^{x} \right)}} + \frac{7 \left(\tan^{2}{\left(x \right)} + 1\right) \sqrt{\cos^{3}{\left(5 x \right)}}}{\log{\left(7 \right)} \tan{\left(x \right)}} - \frac{105 \sqrt{\cos^{3}{\left(5 x \right)}} \log{\left(\tan{\left(x \right)} \right)} \sin{\left(5 x \right)}}{2 \log{\left(7 \right)} \cos{\left(5 x \right)}}$$

Simplify

The second derivative [src]

      ___________                        ___________                                                  _____________        ___________              2                                             _____________                                       2            _____________                     _____________                         ___________                                ___________                                                                  
     /    3       /       2   \         /    3                               /     2\            2 5 /    /     2\        /    3       /       2   \            2    2/     2\       x    2    5 /    /     2\  /       2/ x\\      2*x /       2/ x\\     2    5 /    /     2\       2*x    2    5 /    /     2\  /       2/ x\\         /    3          2                          /    3       /       2   \                 x /       2/ x\\    /     2\       
14*\/  cos (5*x) *\1 + tan (x)/   525*\/  cos (5*x) *log(tan(x))        2*cos\3 + x /         4*x *\/  sin\3 + x /    7*\/  cos (5*x) *\1 + tan (x)/        16*x *cos \3 + x /      7 *log (7)*\/  sin\3 + x / *\1 + tan \7 //   2*7   *\1 + tan \7 // *log (7)*\/  sin\3 + x /    2*7   *log (7)*\/  sin\3 + x / *\1 + tan \7 //   525*\/  cos (5*x) *sin (5*x)*log(tan(x))   105*\/  cos (5*x) *\1 + tan (x)/*sin(5*x)   4*x*7 *\1 + tan \7 //*cos\3 + x /*log(7)
------------------------------- - ------------------------------ - ------------------------ + --------------------- - ------------------------------- + ------------------------- + ------------------------------------------ - ----------------------------------------------- + ---------------------------------------------- + ---------------------------------------- - ----------------------------------------- + ----------------------------------------
             log(7)                          2*log(7)                   4/5/     2\    / x\              / x\                            2                    9/5/     2\    / x\                       2/ x\                                           3/ x\                                            / x\                                       2                                    cos(5*x)*log(7)*tan(x)                        4/5/     2\    2/ x\        
                                                                   5*sin   \3 + x /*tan\7 /         5*tan\7 /                  log(7)*tan (x)           25*sin   \3 + x /*tan\7 /                    tan \7 /                                        tan \7 /                                         tan\7 /                                  4*cos (5*x)*log(7)                                                                 5*sin   \3 + x /*tan \7 /

$$- \frac{2 \cdot 7^{2 x} \left(\tan^{2}{\left(7^{x} \right)} + 1\right)^{2} \log{\left(7 \right)}^{2} \sqrt[5]{\sin{\left(x^{2} + 3 \right)}}}{\tan^{3}{\left(7^{x} \right)}} + \frac{2 \cdot 7^{2 x} \left(\tan^{2}{\left(7^{x} \right)} + 1\right) \log{\left(7 \right)}^{2} \sqrt[5]{\sin{\left(x^{2} + 3 \right)}}}{\tan{\left(7^{x} \right)}} + \frac{4 \cdot 7^{x} x \left(\tan^{2}{\left(7^{x} \right)} + 1\right) \log{\left(7 \right)} \cos{\left(x^{2} + 3 \right)}}{5 \sin^{\frac{4}{5}}{\left(x^{2} + 3 \right)} \tan^{2}{\left(7^{x} \right)}} + \frac{7^{x} \left(\tan^{2}{\left(7^{x} \right)} + 1\right) \log{\left(7 \right)}^{2} \sqrt[5]{\sin{\left(x^{2} + 3 \right)}}}{\tan^{2}{\left(7^{x} \right)}} + \frac{4 x^{2} \sqrt[5]{\sin{\left(x^{2} + 3 \right)}}}{5 \tan{\left(7^{x} \right)}} + \frac{16 x^{2} \cos^{2}{\left(x^{2} + 3 \right)}}{25 \sin^{\frac{9}{5}}{\left(x^{2} + 3 \right)} \tan{\left(7^{x} \right)}} - \frac{7 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \sqrt{\cos^{3}{\left(5 x \right)}}}{\log{\left(7 \right)} \tan^{2}{\left(x \right)}} - \frac{105 \left(\tan^{2}{\left(x \right)} + 1\right) \sqrt{\cos^{3}{\left(5 x \right)}} \sin{\left(5 x \right)}}{\log{\left(7 \right)} \cos{\left(5 x \right)} \tan{\left(x \right)}} + \frac{14 \left(\tan^{2}{\left(x \right)} + 1\right) \sqrt{\cos^{3}{\left(5 x \right)}}}{\log{\left(7 \right)}} + \frac{525 \sqrt{\cos^{3}{\left(5 x \right)}} \log{\left(\tan{\left(x \right)} \right)} \sin^{2}{\left(5 x \right)}}{4 \log{\left(7 \right)} \cos^{2}{\left(5 x \right)}} - \frac{525 \sqrt{\cos^{3}{\left(5 x \right)}} \log{\left(\tan{\left(x \right)} \right)}}{2 \log{\left(7 \right)}} - \frac{2 \cos{\left(x^{2} + 3 \right)}}{5 \sin^{\frac{4}{5}}{\left(x^{2} + 3 \right)} \tan{\left(7^{x} \right)}}$$

Simplify

The third derivative [src]

        _____________         ___________              2                                                          ___________              3         ___________                                ___________                                                                                                                     _____________                         ___________                                                2            _____________                        2            _____________                     _____________                                       3            _____________           ___________                                  ___________                                    _____________                                                                         ___________              2                    ___________                                                                                                 2                                                                                                               
     5 /    /     2\         /    3       /       2   \                      _____________                       /    3       /       2   \         /    3       /       2   \                 /    3       /       2   \            3    3/     2\               3    /     2\                   2/     2\        x    3    5 /    /     2\  /       2/ x\\         /    3       /       2   \                3*x /       2/ x\\     3    5 /    /     2\       2*x /       2/ x\\     3    5 /    /     2\       2*x    3    5 /    /     2\  /       2/ x\\      3*x /       2/ x\\     3    5 /    /     2\           /    3          3                            /    3                                  x  2 5 /    /     2\  /       2/ x\\             x /       2/ x\\    /     2\                /    3       /       2   \                    /    3          2      /       2   \       x  2    2/     2\ /       2/ x\\                2*x /       2/ x\\     2       /     2\        x    2    /       2/ x\\    /     2\         2*x    2    /       2/ x\\    /     2\
12*x*\/  sin\3 + x /    28*\/  cos (5*x) *\1 + tan (x)/       3*x    3    5 /    /     2\  /       2/ x\\   14*\/  cos (5*x) *\1 + tan (x)/    28*\/  cos (5*x) *\1 + tan (x)/*tan(x)   1575*\/  cos (5*x) *\1 + tan (x)/       288*x *cos \3 + x /           56*x *cos\3 + x /           48*x*cos \3 + x /       7 *log (7)*\/  sin\3 + x / *\1 + tan \7 //   315*\/  cos (5*x) *\1 + tan (x)/*sin(5*x)   10*7   *\1 + tan \7 // *log (7)*\/  sin\3 + x /    6*7   *\1 + tan \7 // *log (7)*\/  sin\3 + x /    6*7   *log (7)*\/  sin\3 + x / *\1 + tan \7 //   6*7   *\1 + tan \7 // *log (7)*\/  sin\3 + x /    2625*\/  cos (5*x) *sin (5*x)*log(tan(x))   13125*\/  cos (5*x) *log(tan(x))*sin(5*x)   12*7 *x *\/  sin\3 + x / *\1 + tan \7 //*log(7)   6*7 *\1 + tan \7 //*cos\3 + x /*log(7)   315*\/  cos (5*x) *\1 + tan (x)/ *sin(5*x)   1575*\/  cos (5*x) *sin (5*x)*\1 + tan (x)/   48*7 *x *cos \3 + x /*\1 + tan \7 //*log(7)   12*x*7   *\1 + tan \7 // *log (7)*cos\3 + x /   6*x*7 *log (7)*\1 + tan \7 //*cos\3 + x /   12*x*7   *log (7)*\1 + tan \7 //*cos\3 + x /
--------------------- - -------------------------------- + 4*7   *log (7)*\/  sin\3 + x / *\1 + tan \7 // + -------------------------------- + -------------------------------------- - --------------------------------- - --------------------------- - ------------------------- + ------------------------- + ------------------------------------------ - ----------------------------------------- - ------------------------------------------------ - ----------------------------------------------- + ---------------------------------------------- + ----------------------------------------------- + ----------------------------------------- + ----------------------------------------- - ----------------------------------------------- + -------------------------------------- + ------------------------------------------ + ------------------------------------------- - ------------------------------------------- - --------------------------------------------- + ----------------------------------------- + --------------------------------------------
           / x\                  log(7)*tan(x)                                                                                 3                               log(7)                            2*log(7)*tan(x)                   14/5/     2\    / x\         4/5/     2\    / x\         9/5/     2\    / x\                       2/ x\                                 cos(5*x)*log(7)                                       2/ x\                                              3/ x\                                            / x\                                              4/ x\                                       3                                      4*cos(5*x)*log(7)                                       2/ x\                                4/5/     2\    2/ x\                                       2                             2                                              9/5/     2\    2/ x\                          4/5/     2\    3/ x\                          4/5/     2\    2/ x\                          4/5/     2\    / x\          
      5*tan\7 /                                                                                                      log(7)*tan (x)                                                                                         125*sin    \3 + x /*tan\7 /   25*sin   \3 + x /*tan\7 /   25*sin   \3 + x /*tan\7 /                    tan \7 /                                                                                    tan \7 /                                           tan \7 /                                         tan\7 /                                           tan \7 /                                  8*cos (5*x)*log(7)                                                                             5*tan \7 /                           5*sin   \3 + x /*tan \7 /                  2*cos(5*x)*log(7)*tan (x)                     4*cos (5*x)*log(7)*tan(x)                     25*sin   \3 + x /*tan \7 /                     5*sin   \3 + x /*tan \7 /                     5*sin   \3 + x /*tan \7 /                     5*sin   \3 + x /*tan\7 /

$$\frac{6 \cdot 7^{3 x} \left(\tan^{2}{\left(7^{x} \right)} + 1\right)^{3} \log{\left(7 \right)}^{3} \sqrt[5]{\sin{\left(x^{2} + 3 \right)}}}{\tan^{4}{\left(7^{x} \right)}} - \frac{10 \cdot 7^{3 x} \left(\tan^{2}{\left(7^{x} \right)} + 1\right)^{2} \log{\left(7 \right)}^{3} \sqrt[5]{\sin{\left(x^{2} + 3 \right)}}}{\tan^{2}{\left(7^{x} \right)}} + 4 \cdot 7^{3 x} \left(\tan^{2}{\left(7^{x} \right)} + 1\right) \log{\left(7 \right)}^{3} \sqrt[5]{\sin{\left(x^{2} + 3 \right)}} - \frac{12 \cdot 7^{2 x} x \left(\tan^{2}{\left(7^{x} \right)} + 1\right)^{2} \log{\left(7 \right)}^{2} \cos{\left(x^{2} + 3 \right)}}{5 \sin^{\frac{4}{5}}{\left(x^{2} + 3 \right)} \tan^{3}{\left(7^{x} \right)}} + \frac{12 \cdot 7^{2 x} x \left(\tan^{2}{\left(7^{x} \right)} + 1\right) \log{\left(7 \right)}^{2} \cos{\left(x^{2} + 3 \right)}}{5 \sin^{\frac{4}{5}}{\left(x^{2} + 3 \right)} \tan{\left(7^{x} \right)}} - \frac{6 \cdot 7^{2 x} \left(\tan^{2}{\left(7^{x} \right)} + 1\right)^{2} \log{\left(7 \right)}^{3} \sqrt[5]{\sin{\left(x^{2} + 3 \right)}}}{\tan^{3}{\left(7^{x} \right)}} + \frac{6 \cdot 7^{2 x} \left(\tan^{2}{\left(7^{x} \right)} + 1\right) \log{\left(7 \right)}^{3} \sqrt[5]{\sin{\left(x^{2} + 3 \right)}}}{\tan{\left(7^{x} \right)}} - \frac{12 \cdot 7^{x} x^{2} \left(\tan^{2}{\left(7^{x} \right)} + 1\right) \log{\left(7 \right)} \sqrt[5]{\sin{\left(x^{2} + 3 \right)}}}{5 \tan^{2}{\left(7^{x} \right)}} - \frac{48 \cdot 7^{x} x^{2} \left(\tan^{2}{\left(7^{x} \right)} + 1\right) \log{\left(7 \right)} \cos^{2}{\left(x^{2} + 3 \right)}}{25 \sin^{\frac{9}{5}}{\left(x^{2} + 3 \right)} \tan^{2}{\left(7^{x} \right)}} + \frac{6 \cdot 7^{x} x \left(\tan^{2}{\left(7^{x} \right)} + 1\right) \log{\left(7 \right)}^{2} \cos{\left(x^{2} + 3 \right)}}{5 \sin^{\frac{4}{5}}{\left(x^{2} + 3 \right)} \tan^{2}{\left(7^{x} \right)}} + \frac{7^{x} \left(\tan^{2}{\left(7^{x} \right)} + 1\right) \log{\left(7 \right)}^{3} \sqrt[5]{\sin{\left(x^{2} + 3 \right)}}}{\tan^{2}{\left(7^{x} \right)}} + \frac{6 \cdot 7^{x} \left(\tan^{2}{\left(7^{x} \right)} + 1\right) \log{\left(7 \right)} \cos{\left(x^{2} + 3 \right)}}{5 \sin^{\frac{4}{5}}{\left(x^{2} + 3 \right)} \tan^{2}{\left(7^{x} \right)}} - \frac{56 x^{3} \cos{\left(x^{2} + 3 \right)}}{25 \sin^{\frac{4}{5}}{\left(x^{2} + 3 \right)} \tan{\left(7^{x} \right)}} - \frac{288 x^{3} \cos^{3}{\left(x^{2} + 3 \right)}}{125 \sin^{\frac{14}{5}}{\left(x^{2} + 3 \right)} \tan{\left(7^{x} \right)}} + \frac{12 x \sqrt[5]{\sin{\left(x^{2} + 3 \right)}}}{5 \tan{\left(7^{x} \right)}} + \frac{48 x \cos^{2}{\left(x^{2} + 3 \right)}}{25 \sin^{\frac{9}{5}}{\left(x^{2} + 3 \right)} \tan{\left(7^{x} \right)}} + \frac{14 \left(\tan^{2}{\left(x \right)} + 1\right)^{3} \sqrt{\cos^{3}{\left(5 x \right)}}}{\log{\left(7 \right)} \tan^{3}{\left(x \right)}} + \frac{315 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \sqrt{\cos^{3}{\left(5 x \right)}} \sin{\left(5 x \right)}}{2 \log{\left(7 \right)} \cos{\left(5 x \right)} \tan^{2}{\left(x \right)}} - \frac{28 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \sqrt{\cos^{3}{\left(5 x \right)}}}{\log{\left(7 \right)} \tan{\left(x \right)}} + \frac{1575 \left(\tan^{2}{\left(x \right)} + 1\right) \sqrt{\cos^{3}{\left(5 x \right)}} \sin^{2}{\left(5 x \right)}}{4 \log{\left(7 \right)} \cos^{2}{\left(5 x \right)} \tan{\left(x \right)}} - \frac{315 \left(\tan^{2}{\left(x \right)} + 1\right) \sqrt{\cos^{3}{\left(5 x \right)}} \sin{\left(5 x \right)}}{\log{\left(7 \right)} \cos{\left(5 x \right)}} + \frac{28 \left(\tan^{2}{\left(x \right)} + 1\right) \sqrt{\cos^{3}{\left(5 x \right)}} \tan{\left(x \right)}}{\log{\left(7 \right)}} - \frac{1575 \left(\tan^{2}{\left(x \right)} + 1\right) \sqrt{\cos^{3}{\left(5 x \right)}}}{2 \log{\left(7 \right)} \tan{\left(x \right)}} + \frac{2625 \sqrt{\cos^{3}{\left(5 x \right)}} \log{\left(\tan{\left(x \right)} \right)} \sin^{3}{\left(5 x \right)}}{8 \log{\left(7 \right)} \cos^{3}{\left(5 x \right)}} + \frac{13125 \sqrt{\cos^{3}{\left(5 x \right)}} \log{\left(\tan{\left(x \right)} \right)} \sin{\left(5 x \right)}}{4 \log{\left(7 \right)} \cos{\left(5 x \right)}}$$

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Derivative of 7sqrt(cos(5x)^(3))*log7(tg(x))-(((sin(x^2+3))^0.2)/tg(7^x))

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Derivative of 7*sqrt(cos(5*x)^(3))*log7(tg(x))-(((sin(x^2+3))^0.2)/tg(7^x))

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Derivative of 7sqrt(cos(5x)^(3))*log7(tg(x))-(((sin(x^2+3))^0.2)/tg(7^x))