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

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To implicitly differentiate ( \csc(x^2+y^2)=e^{-xy} ), follow these steps:

- Differentiate both sides of the equation with respect to (x).
- Use the chain rule and the derivative of the cosecant function.
- Solve for the derivative ( \frac{dy}{dx} ).

The result after differentiation is:

( -2x\cot(x^2+y^2) + 2ye^{-xy} = -y\cot(x^2+y^2)e^{-xy} \frac{dx}{dy} )

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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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