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

now differentiate.

now rearrange.

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To implicitly differentiate (4 = y - \frac{e^{2y}}{y-x}), first differentiate both sides of the equation with respect to (x).

The derivative of (4) with respect to (x) is (0) since it's a constant.

For the left side, differentiate (y) with respect to (x) to get (\frac{dy}{dx}).

For the right side, you need to use the quotient rule. Let (u = y - x) and (v = e^{2y}). Then apply the quotient rule (\frac{d}{dx}\left(\frac{u}{v}\right) = \frac{u'v - uv'}{v^2}).

After finding the derivatives, rearrange the equation to solve for (\frac{dy}{dx}).

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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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