Mister Exam

Derivative of 3x^2sinx

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   2       
3*x *sin(x)
$$3 x^{2} \sin{\left(x \right)}$$
d /   2       \
--\3*x *sin(x)/
dx             
$$\frac{d}{d x} 3 x^{2} \sin{\left(x \right)}$$
Detail solution
  1. The derivative of a constant times a function is the constant times the derivative of the function.

    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:

    So, the result is:

  2. Now simplify:


The answer is:

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