# How do you differentiate #e^sqrt(xy)-sqrt(xy)=8#?

See explanation.

#dy/dx = -c/(x^2)#

where

Then the original equation simplifies to:

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To differentiate ( e^{\sqrt{xy}} - \sqrt{xy} = 8 ):

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

The result after differentiation is:

( \frac{1}{2}e^{\sqrt{xy}} \left(\frac{y}{2\sqrt{xy}} + \frac{x}{2\sqrt{xy}} \right) - \frac{1}{2\sqrt{xy}} - \frac{1}{2}\frac{x}{\sqrt{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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