Home > Calculus > Implicit Differentiation

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

Answer 1

Aurora Alvarado

See the answer below:

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Luke Alvarez

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}).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

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.