# How do you implicitly differentiate #-y^2=e^(2x-4y)-2y/x #?

Simplify by dividing by 2

Factor the y'

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To implicitly differentiate -y^2 = e^(2x - 4y) - (2y/x) with respect to x:

- Differentiate both sides of the equation with respect to x.
- Apply the chain rule and the product rule where necessary.
- Solve for dy/dx.

The result is: dy/dx = (4y^2 - 2xe^(2x - 4y) + 2e^(2x - 4y)) / (4y + 2x^2/y)

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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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