Use implicit differentiation to find $\frac { \partial z } { \partial x }$ $x ^ { 4 } y + x z + y z ^ { 2 } = 7$
A) $\frac { \partial z } { \partial x } = - \frac { 4 x ^ { 3 } y } { 1 + 2 y }$
B) $\frac { \partial z } { \partial x } = - \frac { 4 x ^ { 3 } y + z } { x + 2 y z }$
C) $\frac { \partial z } { \partial x } = - \frac { 4 x ^ { 3 } } { 1 + 2 y }$
D) $\frac { \partial z } { \partial x } = \frac { 1 } { 1 + 2 y }$

Question

Quizplus · Accepted Answer

Implicit differentiation of the given equation with respect to $x$ and solving for $\frac{\partial z}{\partial x}$ gives the expression $- \frac { 4 x ^ { 3 } y + z } { x + 2 y z }$.

Use Implicit Differentiation to Find ∂z∂x\frac { \partial z } { \partial x }∂x∂z​

Use Implicit Differentiation to Find $\frac { \partial z } { \partial x }$