$$\text { Use implicit differentiation to find } d y / d x \text { and } \mathrm { d } ^ { 2 } y / d x ^ { 2 } \text {. }$$
-$4 \sqrt { \mathrm { y } } - \mathrm { y } = 2 \mathrm { x }$
A) $\frac { d y } { d x } = \frac { 2 \sqrt { y } } { 2 - \sqrt { y } } ; \frac { d ^ { 2 } y } { d x ^ { 2 } } = \frac { 4 } { ( 2 - \sqrt { y } ) ^ { 3 } }$
B) $\frac { d y } { d x } = \frac { 2 } { \sqrt { y } } - 2 ; \frac { d ^ { 2 } y } { d x ^ { 2 } } = - \frac { 2 } { y ^ { 2 } }$
C) $\frac { d y } { d x } = \frac { 2 - \sqrt { y } } { 2 \sqrt { y } } ; \frac { d ^ { 2 } y } { d x ^ { 2 } } = \frac { 2 - \sqrt { y } } { 4 y }$
D) $\frac { d y } { d x } = \frac { 2 \sqrt { y } } { 2 - \sqrt { y } } ; \frac { d ^ { 2 } y } { d x ^ { 2 } } = \frac { 2 - 2 \sqrt { y } } { \sqrt { y } ( 2 - \sqrt { y } ) ^ { 2 } }$

Question

Quizplus · Accepted Answer

Differentiating both sides of the equation with respect to $x$ gives the first derivative $dy/dx$. For the second derivative $d^2y/dx^2$, differentiate $dy/dx$ with respect to $x$ again, applying the chain rule as necessary.

Use implicit differentiation to find dy/dx and d2y/dx2. \text { Use implicit differentiation to find } d y / d x \text { and } \mathrm { d } ^ { 2 } y / d x ^ { 2 } \text {. } Use implicit differentiation to find dy/dx and d2y/dx2.

$\text { Use implicit differentiation to find } d y / d x \text { and } \mathrm { d } ^ { 2 } y / d x ^ { 2 } \text {. }$