Question

How do you differentiate `sin^2(x) cos (x)`?

Answer 1

`cosxsin2x-sin^3x`

Explanation:

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

`"Given "y=f(x)g(x)" then"`

`dy/dx=f(x)g'(x)+g(x)f'(x)larrcolor(blue)"product rule"`

`"differentiate "sin^2x=(sinx)^2" using "color(blue)"chain rule"`

`"Given "y=f(g(x))" then"`

`dy/dx=f'(g(x))xxg'(x)larrcolor(blue)"chain rule"`

`f(x)=(sinx)^2rArrf'(x)=2sinxcosx=sin2x`

`g(x)=cosxrArrg'(x)=-sinx`

`rArrd/dx(sin^2xcosx)`

`=sin^2x(-sinx)+cosxsin2x`

`=cosxsin2x-sin^3x`