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y=x^2sinx^2

Derivative of y=x^2sinx^2

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

The graph:

from to

Piecewise:

The solution

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

    ; to find :

    1. Apply the power rule: goes to

    ; to find :

    1. Let .

    2. Apply the power rule: goes to

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

      1. The derivative of sine is cosine:

      The result of the chain rule is:

    The result is:

  2. Now simplify:


The answer is:

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