# How do you differentiate #sin^2x-sin^2y=x-y-5#?

Write the equation as:

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Answer:

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To differentiate ( \sin^2x - \sin^2y = x - y - 5 ), you can use implicit differentiation. The derivatives are:

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

Applying implicit differentiation to the equation gives:

[ 2\sin x \cos x - (-2\sin y \cos y) = 1 - 1 ]

Simplifying further, we get:

[ 2\sin x \cos x + 2\sin y \cos y = 0 ]

This is the derivative of the given equation with respect to ( x ) and ( y ).

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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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