# How do you differentiate #e^sqrty-xy=6#?

Use implicit differentiation ...

Using implicit differentiation, chain and product rules :

Finally, solve for y'

hope that helps

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To differentiate ( e^{\sqrt{y}-xy}=6 ) with respect to ( x ), we can use the chain rule and the product rule. The derivative is:

[ \frac{d}{dx} \left( e^{\sqrt{y}-xy} \right) = e^{\sqrt{y}-xy} \left( -y - y'\sqrt{y} \right) ]

where ( y' ) is the derivative of ( y ) with respect to ( x ).

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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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