Question

How do you differentiate `f(x)=(x^2+sinx)(x-cosx)` using the product rule?

Answer 1

`=3x^2-xcosx+(1+x^2)sinx-cos2x`

Explanation:

`f(x)=(x^2+sinx)(x−cosx)`
`f^'(x)=(x^2+sinx)d/dx(x−cosx)+(x−cosx)d/dx(x^2+sinx)`
`=(x^2+sinx)(1+sinx)+(x−cosx)(2x+cosx)`
`=x^2+sinx+x^2sinx+sin^2x+2x^2-2xcosx+xcosx-cos^2x`
`=sin^2x-cos^2x+sinx(1+x^2)-xcosx+3x^2`
`=3x^2-xcosx+(1+x^2)sinx-cos2x`