Question

What is the derivative of `f(x) = sin(x)-cos^2(x)`?

Answer 1

Any of these (all identical):
`f'(x)=cosx+2xcosxsinx`
`f'(x)=cosx(1+2xsinx)`
`f'(x)=cosx+xsin(2x)`

Explanation:

`f'(x)=d/dx[sinx]-d/dx[cos^2x]`

`d/dx[sinx]=cosx`

`d/dx[cos^2x]=2xcosxd/dx[cosx]=-2xcosxsinx`

`f'(x)=cosx-(-2xcosxsinx)`

`f'(x)=cosx+2xcosxsinx=cosx(1+2xsinx)orcosx+xsin(2x)`

Answer 2

See answer below

Explanation:

Given `f(x)=sinx-cos^2x`

Derivative is given by `f´(x)=cosx-2cosx·(-sinx)=2sinxcosx+cosx=sin2x+cosx`