Mister Exam

Derivative of sin(log(x))

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
sin(log(x))
$$\sin{\left(\log{\left(x \right)} \right)}$$
d              
--(sin(log(x)))
dx             
$$\frac{d}{d x} \sin{\left(\log{\left(x \right)} \right)}$$
Detail solution
  1. Let .

  2. The derivative of sine is cosine:

  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]
cos(log(x))
-----------
     x     
$$\frac{\cos{\left(\log{\left(x \right)} \right)}}{x}$$
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]
3*sin(log(x)) + cos(log(x))
---------------------------
              3            
             x             
$$\frac{3 \sin{\left(\log{\left(x \right)} \right)} + \cos{\left(\log{\left(x \right)} \right)}}{x^{3}}$$
The graph
Derivative of sin(log(x))