# How do you implicitly differentiate #18=(y-x)lny-y/x#?

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To implicitly differentiate (18=(y-x)\ln y - \frac{y}{x}), follow these steps:

- Differentiate each term with respect to (x).
- Use the product rule for the first term and the quotient rule for the second term.
- Solve for (\frac{dy}{dx}) after differentiation.

The result of differentiating (18=(y-x)\ln y - \frac{y}{x}) implicitly with respect to (x) is:

[0 = (\ln y + \frac{y}{y})(\frac{dy}{dx}) - \frac{dy}{dx} - \frac{y}{x^2}]

Simplify this 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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