Mister Exam

Derivative of xsin3x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
x*sin(3*x)
$$x \sin{\left(3 x \right)}$$
d             
--(x*sin(3*x))
dx            
$$\frac{d}{d x} x \sin{\left(3 x \right)}$$
Detail solution
  1. Apply the product rule:

    ; to find :

    1. Apply the power rule: goes to

    ; to find :

    1. Let .

    2. The derivative of sine is cosine:

    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]
3*x*cos(3*x) + sin(3*x)
$$3 x \cos{\left(3 x \right)} + \sin{\left(3 x \right)}$$
The second derivative [src]
3*(2*cos(3*x) - 3*x*sin(3*x))
$$3 \left(- 3 x \sin{\left(3 x \right)} + 2 \cos{\left(3 x \right)}\right)$$
The third derivative [src]
-27*(x*cos(3*x) + sin(3*x))
$$- 27 \left(x \cos{\left(3 x \right)} + \sin{\left(3 x \right)}\right)$$
The graph
Derivative of xsin3x