Question

What is the second derivative of `x^2sinx`?

Answer 1

`(d^2y)/(dx^2)=2sinx+4xcosx-x^2sinx`

Explanation:

We have `y=x^2sinx`

`dy/dx=d/dx[x^2]sinx+x^2d/dx[sinx]=2xsinx+x^2cosx`

`(d^2y)/(dx^2)=d/dx[2x]sinx+2xd/dx[sinx]+d/dx[x^2]cosx+x^2d/dx[cosx]=2sinx+2xcosx+2xcosx-x^2sinx=2sinx+4xcosx-x^2sinx`