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Derivative of -2/x
Derivative of 1/(1-x)
Derivative of x^-5
Derivative of x^2*e^x
Identical expressions
y=e^x^ two -7x+ five *tg^3x
y equally e to the power of x squared minus 7x plus 5 multiply by tg cubed x
y equally e to the power of x to the power of two minus 7x plus five multiply by tg cubed x
y=ex2-7x+5*tg3x
y=e^x²-7x+5*tg³x
y=e to the power of x to the power of 2-7x+5*tg to the power of 3x
y=e^x^2-7x+5tg^3x
y=ex2-7x+5tg3x
Similar expressions
y=e^x^2-7x-5*tg^3x
y=e^x^2+7x+5*tg^3x

The derivative of the function/ y=e^x^2-7x+5*tg^3x

Derivative of y=e^x^2-7x+5*tg^3x

The solution

You have entered [src]

 / 2\                  
 \x /              3   
e     - 7*x + 5*tan (x)

$$- 7 x + e^{x^{2}} + 5 \tan^{3}{\left(x \right)}$$

  / / 2\                  \
d | \x /              3   |
--\e     - 7*x + 5*tan (x)/
dx

$$\frac{d}{d x} \left(- 7 x + e^{x^{2}} + 5 \tan^{3}{\left(x \right)}\right)$$

Transform

Detail solution

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

$2 x e^{x^{2}} - 7 + \frac{15 \tan^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}}$

The answer is:

$2 x e^{x^{2}} - 7 + \frac{15 \tan^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

          / 2\                            
          \x /        2    /         2   \
-7 + 2*x*e     + 5*tan (x)*\3 + 3*tan (x)/

$$2 x e^{x^{2}} + 5 \cdot \left(3 \tan^{2}{\left(x \right)} + 3\right) \tan^{2}{\left(x \right)} - 7$$

Simplify

The second derivative [src]

  /      / 2\                   2                                      / 2\\
  |   2  \x /      /       2   \                 3    /       2   \    \x /|
2*\2*x *e     + 15*\1 + tan (x)/ *tan(x) + 15*tan (x)*\1 + tan (x)/ + e    /

$$2 \cdot \left(2 x^{2} e^{x^{2}} + 15 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \tan{\left(x \right)} + 15 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{3}{\left(x \right)} + e^{x^{2}}\right)$$

Simplify

The third derivative [src]

  /                3         / 2\        / 2\                                               2        \
  |   /       2   \       3  \x /        \x /         4    /       2   \       /       2   \     2   |
2*\15*\1 + tan (x)/  + 4*x *e     + 6*x*e     + 30*tan (x)*\1 + tan (x)/ + 105*\1 + tan (x)/ *tan (x)/

$$2 \cdot \left(4 x^{3} e^{x^{2}} + 6 x e^{x^{2}} + 15 \left(\tan^{2}{\left(x \right)} + 1\right)^{3} + 105 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \tan^{2}{\left(x \right)} + 30 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{4}{\left(x \right)}\right)$$

Simplify

The graph

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Derivative of y=e^x^2-7x+5*tg^3x

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The solution