How do you differentiate #y=cos^2(x^2-2)#?

Answer 1

Emily Ammerman

#y'=-4xsin(x^2-2)cos(x^2-2)#

You would use the power rule:

#f(x)=x^n->f'(x)=n*x^(n-1)#

#f(x)=g(x)^n->f'(x)=n*g(x)^(n-1)*g'(x)#

and the chain rule

#f(x)=cos(g(x))->f'(x)=-sin(g(x))*g'(x)#

Then it is:

#y'=2cos(x^2-2)*(-sin(x^2-2))*2x#

#y'=-4xsin(x^2-2)cos(x^2-2)#

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Answer 2

Emilia Aguilar

To differentiate ( y = \cos^2(x^2 - 2) ), use the chain rule.

( \frac{dy}{dx} = -2x \sin(2x^2 - 4) )

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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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