Mister Exam

Derivative of sinx*lnx

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

The graph:

from to

Piecewise:

The solution

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

    ; to find :

    1. The derivative of sine is cosine:

    ; to find :

    1. The derivative of is .

    The result is:


The answer is:

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