Mister Exam

Derivative of x^2sinx

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

The graph:

from to

Piecewise:

The solution

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

    ; to find :

    1. Apply the power rule: goes to

    ; to find :

    1. The derivative of sine is cosine:

    The result is:

  2. Now simplify:


The answer is:

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