Question

How do you differentiate `f(x)=(x+sinx)(x-cosx)` using the product rule?

Answer 1

`f=x+sinx, g=x-cosx; ---- >f'=1+cosx, g'=1+sinx`
`f'(x)=fg'+gf'=(x+sinx)(1+sinx)+(x-cosx)(1+cosx)`

Explanation:

Separate the products into f and g then find the derivative of each separately and put it in to the product rule