# How do you implicitly differentiate #csc(x^2/y^2)=e^(xy) #?

Common denominators:

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To implicitly differentiate ( \csc(x^2/y^2) = e^{xy} ), first, apply the chain rule and the derivative of ( \csc(u) ), where ( u = x^2/y^2 ). Then differentiate ( e^{xy} ) with respect to ( x ).

The result after implicit differentiation is:

[ \frac{-2x \cot(x^2/y^2)}{y^2} - y^2 e^{xy} = 0 ]

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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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