Mister Exam

Derivative of y=x*sin(2*x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
x*sin(2*x)
$$x \sin{\left(2 x \right)}$$
d             
--(x*sin(2*x))
dx            
$$\frac{d}{d x} x \sin{\left(2 x \right)}$$
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]
2*x*cos(2*x) + sin(2*x)
$$2 x \cos{\left(2 x \right)} + \sin{\left(2 x \right)}$$
The second derivative [src]
4*(-x*sin(2*x) + cos(2*x))
$$4 \left(- x \sin{\left(2 x \right)} + \cos{\left(2 x \right)}\right)$$
3-th derivative [src]
-4*(3*sin(2*x) + 2*x*cos(2*x))
$$- 4 \cdot \left(2 x \cos{\left(2 x \right)} + 3 \sin{\left(2 x \right)}\right)$$
The third derivative [src]
-4*(3*sin(2*x) + 2*x*cos(2*x))
$$- 4 \cdot \left(2 x \cos{\left(2 x \right)} + 3 \sin{\left(2 x \right)}\right)$$
The graph
Derivative of y=x*sin(2*x)