Question

How do you differentiate `f(x)=xsinx-e^x*cosx` using the product rule?

Answer 1

I found: `sin(x)[1+e^x]+cos(x)[x-e^x]`

Explanation:

The Product Rule tells us that given:
`f(x)=g(x)h(x)`
Tge derivative will be:
`f'(x)=g'(x)h(x)+g(x)h'(x)`
In your case:
`f'(x)=1*sin(x)+x*cos(x)-e^x*cos(x)+e^x*sin(x)=`
`=sin(x)[1+e^x]+cos(x)[x-e^x]`