Question

How do you differentiate `f(x)=sin^3xcosx`?

Answer 1

`f'(x)=3sin^2xcos^2x-sin^4x`

Explanation:

`"differentiate using the "color(blue)"product rule"`

`"given " f(x)=g(x).h(x)" then"`

`f'(x)=g(x)h'(x)+h(x)g'(x)larr" product rule"`

`g(x)=sin^3x=(sinx)^3`

`"differentiate using the "color(blue)"chain rule"`

`g'(x)=3(sinx)^2xxd/dx(sinx)=3sin^2xcosx`

`h(x)=cosxrArrh'(x)=-sinx`

`rArrf'(x)=sin^3x(-sinx)+3sin^2xcosx(cosx)`

`color(white)(rArrf'(x))=3sin^2cos^2x-sin^4x`