Mister Exam

Derivative of cos(log(x))

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
cos(log(x))
$$\cos{\left(\log{\left(x \right)} \right)}$$
cos(log(x))
Detail solution
  1. Let .

  2. The derivative of cosine is negative sine:

  3. Then, apply the chain rule. Multiply by :

    1. The derivative of is .

    The result of the chain rule is:


The answer is:

The graph
The first derivative [src]
-sin(log(x)) 
-------------
      x      
$$- \frac{\sin{\left(\log{\left(x \right)} \right)}}{x}$$
The second derivative [src]
-cos(log(x)) + sin(log(x))
--------------------------
             2            
            x             
$$\frac{\sin{\left(\log{\left(x \right)} \right)} - \cos{\left(\log{\left(x \right)} \right)}}{x^{2}}$$
The third derivative [src]
-sin(log(x)) + 3*cos(log(x))
----------------------------
              3             
             x              
$$\frac{- \sin{\left(\log{\left(x \right)} \right)} + 3 \cos{\left(\log{\left(x \right)} \right)}}{x^{3}}$$
The graph
Derivative of cos(log(x))