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

How do find the derivative of # y = cos^2(x)#?

Answer 1

Christopher Agresta

First of all #y=cos^2x=(cosx)^2#

Hence

#y'=2cosx*(cosx)'=2cosx*(-sinx)=-2cosx*sinx=-sin2x#

An additional method is

#y=cos^2x=1/2(1+cos2x)#

Hence

#y'=1/2*(-sin2x *(2x)')=-sin2x#

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Answer 2

Isaiah Allen

To find the derivative of ( y = \cos^2(x) ), you can use the chain rule. The derivative is:

[ \frac{dy}{dx} = -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.

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