Question

How do you differentiate `Y = (cos x)^2 - cos x`?

Answer 1

`dy/dx=sinx-sin2x`

Explanation:

`"differentiate "(cosx)^2" using the "color(blue)"chain rule"`

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

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

`rArrd/dx((cosx)^2)=2cosx xxd/dx(cosx)`

`color(white)(xxxxxxxxxxxx)=-2sinxcosx=-sin2x`

`y=(cosx)^2-cosx`

`rArrdy/dx=-sin2x-(-sinx)`

`color(white)(rArrdy/dx)=sinx-sin2x`