Mister Exam

Derivative of cos(x)*log(x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
cos(x)*log(x)
$$\log{\left(x \right)} \cos{\left(x \right)}$$
cos(x)*log(x)
Detail solution
  1. Apply the product rule:

    ; to find :

    1. The derivative of cosine is negative sine:

    ; to find :

    1. The derivative of is .

    The result is:


The answer is:

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