Question

How do you differentiate `f(x)=xe^xsinx`?

Answer 1

Your regular multiplication rule

Explanation:

We just use the general rule of multiplicative derivatives.
`f(x)=g(x)h(x)`
`f'(x)=g'(x)h(x)+g(x)h'(x)`
The same is standard for a three part function
`f(x)=g(x)h(x)i(x)`
`f'(x)=g'(x)h(x)i(x)+g(x)h'(x)i(x)+g(x)h(x)i'(x)`
We can get the answer simply using that statement.

`f(x)=xe^xsinx`
`f'(x)=(x)'e^xsinx+x(e^x)'sinx+xe^x(sinx)'`
`f'(x)=e^xsinx+xe^xsinx+xe^xcosx`