Find dy/dx by implicit differentiation. $5 x^{2}+9 y^{2}=5$
A) $\frac{5-10 x}{18 y}$
B) $-\frac{5 x}{9 y}$
C) $-\frac{5 x}{9}$
D) $\frac{5-10 x}{18}$

Question

Quizplus · Accepted Answer

We start by using the chain rule:

$\frac{d}{dx}(5x^2 + 9y^2) = \frac{d}{dx}(5)$

$10x\frac{dx}{dx} + 18y\frac{dy}{dx} = 0$

Solving for $\frac{dy}{dx}$:

$18y\frac{dy}{dx} = -10x$

$\frac{dy}{dx} = -\frac{5x}{9y}$

Therefore, the answer is B.

Find Dy/dx by Implicit Differentiation 5x2+9y2=55 x^{2}+9 y^{2}=55x2+9y2=5 A) 5−10x18y\frac{5-10 x}{18 y}18y5−10x​