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

Answer 1

Ezra Adams

The answer #f'(x)=4*sin(x)*cos(x)#

display below

#f(x)=sin^2(x)-cos^2(x)#

#f'(x)=2*sin(x)*cos(x)-[2*cos(x)*-sin(x)]#

#f'(x)=2*sin(x)*cos(x)+2*sin(x)*cos(x)#

#f'(x)=4*sin(x)*cos(x)#

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Answer 2

Aurora Alvarado

To find the derivative of ( f(x) = \sin^2(x) - \cos^2(x) ), differentiate each term separately using the chain rule and the power rule.

Differentiate ( \sin^2(x) ): [ \frac{d}{dx} \sin^2(x) = 2\sin(x) \cos(x) ]
Differentiate ( \cos^2(x) ): [ \frac{d}{dx} \cos^2(x) = -2\sin(x) \cos(x) ]

Combine these results to find the derivative of ( f(x) ): [ f'(x) = 2\sin(x) \cos(x) + 2\sin(x) \cos(x) ] [ f'(x) = 4\sin(x) \cos(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.