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

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To differentiate ( f(x) = \cos^2(x) - \cos(x^2) ), apply the chain rule and the power rule as follows:

- Differentiate each term:

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

- Apply the chain rule and power rule:

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

- Simplify:

[ -2\cos(x)\sin(x) + 2x\sin(x^2)\sin(x^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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