Question

Use implicit defferentiation to determine the derivative of the equation of the eclipse below: 
(X/a)^2+(y/b)^2=1

Answer 1

$$(x/a)^2+(y/b)^2=1$$

Differentiate both sides with respect to $x$

$$\dfrac{d}{dx}((\dfrac{x}{a})^2+(\dfrac{y}{b})^2)=\dfrac{d}{dx}(1)$$

Use the Chain Rule

$$\dfrac{2x}{a^2}+\dfrac{2y}{b^2}\cdot\dfrac{dy}{dx}=0$$

Solve for $\dfrac{dy}{dx}$

$$\dfrac{dy}{dx}=-\dfrac{b^2x}{a^2y}$$