Question

suppose that x and y are related by the equation $5x^2 - 3y^2 = 4$ and use implicit differentiation to determine $\frac{dy}{dx}$.
$\frac{dy}{dx} = \square$

Explanation:

Step1: Differentiate both sides w.r.t. x

Differentiate $5x^2 - 3y^2 = 4$:
$10x - 6y \frac{dy}{dx} = 0$

Step2: Solve for $\frac{dy}{dx}$

Rearrange terms:
$-6y \frac{dy}{dx} = -10x$
Divide both sides by $-6y$:
$\frac{dy}{dx} = \frac{10x}{6y} = \frac{5x}{3y}$

Answer:

$\frac{5x}{3y}$