Question

How do you differentiate `g(x) =x^2sinx` using the product rule?

Answer 1

The trick is to find the two functions where product rule can be applied. Please go through the explanation for the step by step application of the product rule.

Explanation:

The product rule where `u` and `v` are functions of `x`

`(uv)' = u'v+v'u`

The given problem is `g(x) = x^2 sin(x)`

`g(x)=(uv)`
`u=x^2` and `v=sin(x)`

Now to find `u'` and `v'`

`u=x^2`
`u'=2x`

`v=sin(x)`
`v'=cos(x)`

`g'(x) =(uv)' = (2x)(sin(x)) + x^2cos(x)`

`g'(x) = 2xsin(x)+x^2cos(x)` Answer