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Identical expressions
-(ln(cos(three x)))/3
minus (ln( co sinus of e of (3x))) divide by 3
minus (ln( co sinus of e of (three x))) divide by 3
-lncos3x/3
-(ln(cos(3x))) divide by 3
Similar expressions
(ln(cos(3x)))/3

The derivative of the function/ -(ln(cos(3x)))/3

Derivative of -(ln(cos(3x)))/3

The solution

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-log(cos(3*x)) 
---------------
       3

$$\frac{\left(-1\right) \log{\left(\cos{\left(3 x \right)} \right)}}{3}$$

(-log(cos(3*x)))/3

Detail solution

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. Let $u = \cos{\left(3 x \right)}$ .
  2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \cos{\left(3 x \right)}$ :
    1. Let $u = 3 x$ .
    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 $\frac{d}{d x} 3 x$ :
      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: $3$
      The result of the chain rule is:
      
      $- 3 \sin{\left(3 x \right)}$
    The result of the chain rule is:
    
    $- \frac{3 \sin{\left(3 x \right)}}{\cos{\left(3 x \right)}}$
  So, the result is: $\frac{3 \sin{\left(3 x \right)}}{\cos{\left(3 x \right)}}$
So, the result is: $\frac{\sin{\left(3 x \right)}}{\cos{\left(3 x \right)}}$
Now simplify:

$\tan{\left(3 x \right)}$

The answer is:

$\tan{\left(3 x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

sin(3*x)
--------
cos(3*x)

$$\frac{\sin{\left(3 x \right)}}{\cos{\left(3 x \right)}}$$

Simplify

The second derivative [src]

  /       2     \
  |    sin (3*x)|
3*|1 + ---------|
  |       2     |
  \    cos (3*x)/

$$3 \left(\frac{\sin^{2}{\left(3 x \right)}}{\cos^{2}{\left(3 x \right)}} + 1\right)$$

Simplify

The third derivative [src]

   /       2     \         
   |    sin (3*x)|         
18*|1 + ---------|*sin(3*x)
   |       2     |         
   \    cos (3*x)/         
---------------------------
          cos(3*x)

$$\frac{18 \left(\frac{\sin^{2}{\left(3 x \right)}}{\cos^{2}{\left(3 x \right)}} + 1\right) \sin{\left(3 x \right)}}{\cos{\left(3 x \right)}}$$

Simplify

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Derivative of -(ln(cos(3x)))/3

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The solution