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

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Answer 1 · 2018-05-17T11:33:46

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

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

$d/dx[sinx]=cosx$

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

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

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

Answer 2 · 2018-05-17T11:35:54

See answer below

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

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

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