# How do you find the derivative of #cos^2(x^2-2)#?

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To find the derivative of ( \cos^2(x^2-2) ), you can use the chain rule and the derivative of the cosine function. The chain rule states that if ( f(x) = g(h(x)) ), then ( f'(x) = g'(h(x)) \cdot h'(x) ).

First, differentiate the outer function ( \cos^2(u) ) with respect to its inner function ( u ), which is ( x^2 - 2 ). Then, differentiate the inner function ( x^2 - 2 ) with respect to ( x ).

So, the derivative of ( \cos^2(x^2-2) ) with respect to ( x ) is:

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

Simplified, it becomes:

[ -4x\cos(x^2-2)\sin(x^2-2) ]

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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.

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.

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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