Find the derivative of y with respect to x.
-$$y = \tan ^ { - 1 } \sqrt { 5 x }$$
A) $\frac { 1 } { 1 + 5 x }$
B) $\frac { 1 } { 10 \sqrt { 5 x ( 1 + 5 x ) } }$
C) $\frac { 1 } { \sqrt { 1 - 5 x } }$
D) $\frac { 5 } { 2 ( 1 + 5 x ) \sqrt { 5 x } }$

Question

Quizplus · Accepted Answer

To find the derivative of $y = \tan^{-1}(\sqrt{5x})$, we use the chain rule. The derivative of $\tan^{-1}u$ with respect to $u$ is $\frac{1}{1+u^2}$. Let $u = \sqrt{5x}$, then $u^2 = 5x$, and the derivative of $u$ with respect to $x$ is $\frac{1}{2}\sqrt{5/x}$. Applying the chain rule, the derivative of $y$ with respect to $x$ is $\frac{1}{1+5x} \cdot \frac{5}{2\sqrt{5x}} = \frac{5}{2(1+5x)\sqrt{5x}}$.

Find the Derivative of Y with Respect to X y=tan⁡−15xy = \tan ^ { - 1 } \sqrt { 5 x }y=tan−15x​

Find the Derivative of Y with Respect to X $y = \tan ^ { - 1 } \sqrt { 5 x }$