Provide an appropriate answer.
-Find $\frac { \partial z } { \partial v }$ when $u = 5$ and $v = 1$ if $z ( x ) = \frac { x } { \sqrt { x + 5 } }$ and $x = u \cdot v$.
A) $\frac { \partial \mathrm { z } } { \partial \mathrm { v } } = \frac { 75 } { 2 ( 10 ) ^ { 3 / 2 } }$
B) $\frac { \partial z } { \partial v } = \frac { 75 } { 2 \sqrt { 10 } }$
C) $\frac { \partial \mathrm { z } } { \partial \mathrm { v } } = 0$
D) $\frac { \partial \mathrm { z } } { \partial \mathrm { v } } = \frac { 15 } { 2 ( 10 ) ^ { 3 / 2 } }$

Question

Quizplus · Accepted Answer

Given $z(x) = \frac{x}{\sqrt{x+5}}$ and $x = uv$, we first find $\frac{\partial z}{\partial x}$ and then use the chain rule to find $\frac{\partial z}{\partial v}$ by multiplying $\frac{\partial z}{\partial x}$ by $\frac{\partial x}{\partial v}$. With $u=5$ and $v=1$, $x=5\cdot1=5$. The correct differentiation and substitution lead to the answer $\frac{75}{2(10)^{3/2}}$.

Provide an Appropriate Answer ∂z∂v\frac { \partial z } { \partial v }∂v∂z​

Provide an Appropriate Answer $\frac { \partial z } { \partial v }$