How do you find the derivative of (cos x)^2 - cos x?

1 Answer
Jan 24, 2016

sinx-sin2x

Explanation:

To differentiate the squared cosine function, use the chain rule, in that d/dxu^2=2u*u', where u=cosx. This gives us a derivative of

2cosxd/dxcosx-d/dxcosx

Which simplifies to be

2cosx(-sinx)-(-sinx)

or

mathbf(-2cosxsinx+sinx

Note that this can be factored as

sinx(1-2cosx)

or recognize that 2cosxsinx=sin2x, so the derivative equals

sinx-sin2x