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How do you find the derivative of #cos^4(x)-sin^4(x)#?

Answer 1

Isabella Ackerman

#f^'(x)=-2sin2x#

Given #f(x)=(cos^4x-sin^4x)#

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

#=>f(x)=(cos^2x-sin^2x)*1#

#=>f(x)=cos2x#

Differentiating w.r.to x using chain rule #=>f^'(x)=d/"dx"(cos2x)=-sin(2x)d/"dx"(2x)#

#=>f^'(x)=-2sin2x#

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Answer 2

Paisley Johnson

To find the derivative of ( \cos^4(x) - \sin^4(x) ), you can use the chain rule and the power rule. The derivative is ( -4\cos^3(x)\sin(x) + 4\sin^3(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.