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

1 Answer
May 13, 2018

=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