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Derivative of:
Derivative of x^3*lnx
Derivative of x^2/cosx
Derivative of cosu
Derivative of (ax+b)^n
Identical expressions
lncos(two x- one / seven)+2
ln co sinus of e of (2x minus 1 divide by 7) plus 2
ln co sinus of e of (two x minus one divide by seven) plus 2
lncos2x-1/7+2
lncos(2x-1 divide by 7)+2
Similar expressions
lncos(2x-1/7)-2
lncos(2x+1/7)+2

The derivative of the function/ lncos(2x-1/7)+2

Derivative of lncos(2x-1/7)+2

The solution

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log(cos(2*x - 1/7)) + 2

$$\log{\left(\cos{\left(2 x - \frac{1}{7} \right)} \right)} + 2$$

log(cos(2*x - 1/7)) + 2

Detail solution

Differentiate $\log{\left(\cos{\left(2 x - \frac{1}{7} \right)} \right)} + 2$ term by term:
1. Let $u = \cos{\left(2 x - \frac{1}{7} \right)}$ .
2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \cos{\left(2 x - \frac{1}{7} \right)}$ :
  1. Let $u = 2 x - \frac{1}{7}$ .
  2. The derivative of cosine is negative sine:
    
    $\frac{d}{d u} \cos{\left(u \right)} = - \sin{\left(u \right)}$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(2 x - \frac{1}{7}\right)$ :
    1. Differentiate $2 x - \frac{1}{7}$ term by term:
      1. 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: $2$
      2. The derivative of the constant $- \frac{1}{7}$ is zero.
      The result is: $2$
    The result of the chain rule is:
    
    $- 2 \sin{\left(2 x - \frac{1}{7} \right)}$
  The result of the chain rule is:
  
  $- \frac{2 \sin{\left(2 x - \frac{1}{7} \right)}}{\cos{\left(2 x - \frac{1}{7} \right)}}$
4. The derivative of the constant $2$ is zero.
The result is: $- \frac{2 \sin{\left(2 x - \frac{1}{7} \right)}}{\cos{\left(2 x - \frac{1}{7} \right)}}$
Now simplify:

$- 2 \tan{\left(2 x - \frac{1}{7} \right)}$

The answer is:

$- 2 \tan{\left(2 x - \frac{1}{7} \right)}$

The graph

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The first derivative [src]

-2*sin(2*x - 1/7)
-----------------
  cos(2*x - 1/7)

$$- \frac{2 \sin{\left(2 x - \frac{1}{7} \right)}}{\cos{\left(2 x - \frac{1}{7} \right)}}$$

Simplify

The second derivative [src]

   /       2            \
   |    sin (-1/7 + 2*x)|
-4*|1 + ----------------|
   |       2            |
   \    cos (-1/7 + 2*x)/

$$- 4 \left(\frac{\sin^{2}{\left(2 x - \frac{1}{7} \right)}}{\cos^{2}{\left(2 x - \frac{1}{7} \right)}} + 1\right)$$

Simplify

The third derivative [src]

    /       2            \                
    |    sin (-1/7 + 2*x)|                
-16*|1 + ----------------|*sin(-1/7 + 2*x)
    |       2            |                
    \    cos (-1/7 + 2*x)/                
------------------------------------------
             cos(-1/7 + 2*x)

$$- \frac{16 \left(\frac{\sin^{2}{\left(2 x - \frac{1}{7} \right)}}{\cos^{2}{\left(2 x - \frac{1}{7} \right)}} + 1\right) \sin{\left(2 x - \frac{1}{7} \right)}}{\cos{\left(2 x - \frac{1}{7} \right)}}$$

Simplify

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Derivative of lncos(2x-1/7)+2

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The solution