Suppose that x and y are related by the equation $\frac { x ^ { 2 } } { 4 }$ + $\frac { y ^ { 3 } } { 2 }$ = 4. Use implicit differentiation to determine $\frac { d y } { d x }$ .
A) $\frac { d y } { d x }$ = - $\frac { 2 x } { y ^ { 3 } }$
B) $\frac { d y } { d x }$ = $\frac { 2 y ^ { 2 } } { x }$
C) $\frac { d y } { d x }$ = $\frac { 1 } { 3 y ^ { 2 } }$ , y ≠ 0
D) $\frac { d y } { d x }$ = - $\frac { x } { 3 y ^ { 2 } }$ , y ≠ 0

Question

Quizplus · Accepted Answer

Differentiating both sides of the equation with respect to x gives $\frac{1}{2}x\frac{dx}{dx} + \frac{3}{2}y^2\frac{dy}{dx} = 0$. Solving for $\frac{dy}{dx}$ yields $\frac{dy}{dx} = -\frac{x}{3y^2}$, assuming y ≠ 0 to avoid division by zero.

Suppose That X and Y Are Related by the Equation x24\frac { x ^ { 2 } } { 4 }4x2​

Suppose That X and Y Are Related by the Equation $\frac { x ^ { 2 } } { 4 }$