# How do you differentiate #sinx-siny=x-y-5#?

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To differentiate the equation ( \sin(x) - \sin(y) = x - y - 5 ), you can use implicit differentiation. The derivative of ( \sin(x) ) is ( \cos(x) ) and the derivative of ( \sin(y) ) is ( \cos(y) ). Therefore, the derivative of the left side with respect to ( x ) is ( \cos(x) ) and the derivative of the right side with respect to ( x ) is ( 1 ). Similarly, the derivative of the left side with respect to ( y ) is ( -\cos(y) ) and the derivative of the right side with respect to ( y ) is ( -1 ). So, the differentiated equation is ( \cos(x) - \cos(y) = 1 ).

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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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