Question

How do you find the derivative of `f(x)=8sinxcosx`?

Answer 1

`f'(x)=8(cos^2x-sin^2x)=8cos2x`

Explanation:

This will need the product rule:

`f(x)=uv=>f'(x)=vu'+uv'`

`f(x)=8sinxcosx`

`u=8sinx=>u'=8cosx`

`v=cosx=>v'=-sinx`

`:.f'(x)=8cosxxxcosx+8sinx xx(-sinx)`

`f'(x)=8(cos^2x-sin^2x)=8cos2x`