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x^2*sin(2*x)

Derivative of x^2*sin(2*x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
 2         
x *sin(2*x)
$$x^{2} \sin{\left(2 x \right)}$$
x^2*sin(2*x)
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:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
                  2         
2*x*sin(2*x) + 2*x *cos(2*x)
$$2 x^{2} \cos{\left(2 x \right)} + 2 x \sin{\left(2 x \right)}$$
The second derivative [src]
  /     2                                   \
2*\- 2*x *sin(2*x) + 4*x*cos(2*x) + sin(2*x)/
$$2 \left(- 2 x^{2} \sin{\left(2 x \right)} + 4 x \cos{\left(2 x \right)} + \sin{\left(2 x \right)}\right)$$
The third derivative [src]
  /                               2         \
4*\3*cos(2*x) - 6*x*sin(2*x) - 2*x *cos(2*x)/
$$4 \left(- 2 x^{2} \cos{\left(2 x \right)} - 6 x \sin{\left(2 x \right)} + 3 \cos{\left(2 x \right)}\right)$$
The graph
Derivative of x^2*sin(2*x)