Mister Exam

Derivative of y=sinx*log2x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
sin(x)*log(2*x)
$$\log{\left(2 x \right)} \sin{\left(x \right)}$$
d                  
--(sin(x)*log(2*x))
dx                 
$$\frac{d}{d x} \log{\left(2 x \right)} \sin{\left(x \right)}$$
Detail solution
  1. Apply the product rule:

    ; to find :

    1. The derivative of sine is cosine:

    ; to find :

    1. Let .

    2. The derivative of is .

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

      1. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

      The result of the chain rule is:

    The result is:


The answer is:

The graph
The first derivative [src]
sin(x)                  
------ + cos(x)*log(2*x)
  x                     
$$\log{\left(2 x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}$$
The second derivative [src]
  sin(x)                     2*cos(x)
- ------ - log(2*x)*sin(x) + --------
     2                          x    
    x                                
$$- \log{\left(2 x \right)} \sin{\left(x \right)} + \frac{2 \cos{\left(x \right)}}{x} - \frac{\sin{\left(x \right)}}{x^{2}}$$
The third derivative [src]
                   3*sin(x)   3*cos(x)   2*sin(x)
-cos(x)*log(2*x) - -------- - -------- + --------
                      x           2          3   
                                 x          x    
$$- \log{\left(2 x \right)} \cos{\left(x \right)} - \frac{3 \sin{\left(x \right)}}{x} - \frac{3 \cos{\left(x \right)}}{x^{2}} + \frac{2 \sin{\left(x \right)}}{x^{3}}$$
The graph
Derivative of y=sinx*log2x