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

1 Answer
Nov 20, 2017

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