Home > Calculus > Derivative Rules for y=cos(x) and y=tan(x)

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

Answer 1

Cameron Alexander

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)#

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Answer 2

Christopher Allers

See answer below

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

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

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Answer 3

Samantha Adkison

The derivative of ( f(x) = \sin(x) - \cos^2(x) ) is ( f'(x) = \cos(x) + 2\cos(x)\sin(x) ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.