If $y=\log \sqrt{ an x}$, then the value of $\frac{d y}{d x}$ at $x=\frac{\pi}{4}$ is

Question

If $y=\log \sqrt{	an x}$, then the value of $\frac{d y}{d x}$ at $x=\frac{\pi}{4}$ is

Aicharya · Accepted Answer

$\begin{aligned} & y=\log \sqrt{	an x} \ & 	herefore \quad \frac{d y}{d x}=\frac{1}{\sqrt{	an x}} 	imes \frac{1}{2 \sqrt{	an x}} 	imes \sec ^2 x=\frac{\sec ^2 x}{2 	an x} \ & 	herefore \quad\left(\frac{d y}{d x}ight)_{x=\frac{\pi}{4}}=\frac{(\sqrt{2})^2}{2}=1\end{aligned}$

If $y=\log \sqrt{\tan x}$, then the value of $\frac{d y}{d x}$ at $x=\frac{\pi}{4}$ is

Solution