Question

How do you find the derivative of `x^2 sinx`?

Answer 1

`d/dx(x^2sinx)=2xsinx+x^2cosx`

Explanation:

The product rule states that:
`d/dx(uv)=u'v+uv'`
Where `u` and `v` are functions of `x`.

In `x^2sinx`, we have two functions: `x^2` and `sinx`. Since they are being multiplied together, we'll need to use the product rule to find the derivative.

Let `u=x^2` and `v=sinx`:
`u=x^2->u'=2x`
`v=sinx->v'=cosx`

Making necessary substitutions in the product rule, we have:
`(2x)(sinx)+(x^2)(cosx)`
`=2xsinx+x^2cosx`

We can't really simplify this further, so we'll leave it as our final answer.