Question

How do you differentiate `g(x)=xsinx` using the product rule?

Answer 1

`g'(x) = xcosx+sinx`

Explanation:

The Product Rule states that for a function of the form: `f(x)h(x)`

then `d/dxf(x)h(x) = f(x)h'(x)+f'(x)h(x)`
[NB: This is often written with `f(x)` and `g(x)` but that would have been confusing here as the funtion in the question is labelled `g(x)`]

In this example `f(x) = x` and `h(x) = sinx`

`:. g'(x) = x* d/dx(sinx) + d/dx(x)* sinx`

`= x*cosx + 1*sinx`

`= xcosx+sinx`