Find the partial derivative $$\frac { \partial z } { \partial x } \text { for the function } z = 26 y ^ { 2 } \sqrt { x }$$
A)$\frac { \partial z } { \partial x } = \frac { 13 y ^ { 2 } } { \sqrt { x } }$
B) $\frac { \partial z } { \partial x } = \frac { 26 } { \sqrt { x } }$
C) $\frac { \partial z } { \partial x } = 13 y ^ { 2 } \sqrt { x }$
D) $\frac { \partial z } { \partial x } = \frac { 13 } { x }$
E) $\frac { \partial z } { \partial x } = 13 y ^ { 2 }$

Question

Find the partial derivative $$\frac { \partial z } { \partial x } \text { for the function } z = 26 y ^ { 2 } \sqrt { x }$$ 
A)$\frac { \partial z } { \partial x } = \frac { 13 y ^ { 2 } } { \sqrt { x } }$
B) $\frac { \partial z } { \partial x } = \frac { 26 } { \sqrt { x } }$
C) $\frac { \partial z } { \partial x } = 13 y ^ { 2 } \sqrt { x }$
D) $\frac { \partial z } { \partial x } = \frac { 13 } { x }$
E) $\frac { \partial z } { \partial x } = 13 y ^ { 2 }$

Quizplus · Accepted Answer

To find the partial derivative of $z = 26y^2\sqrt{x}$ with respect to $x$, treat $y$ as a constant and apply the derivative rule for $x^n$, which gives $\frac{1}{2} \cdot 26y^2 \cdot x^{-1/2} = \frac{13y^2}{\sqrt{x}}$.

Find the Partial Derivative ∂z∂x for the function z=26y2x\frac { \partial z } { \partial x } \text { for the function } z = 26 y ^ { 2 } \sqrt { x }∂x∂z​ for the function z=26y2x​

Find the Partial Derivative $\frac { \partial z } { \partial x } \text { for the function } z = 26 y ^ { 2 } \sqrt { x }$