MHT CET · Maths · Differentiation
If \(y=\log \sqrt{\tan x}\), then the value of \(\frac{d y}{d x}\) at \(x=\frac{\pi}{4}\) is
- A 1
- B \(-1\)
- C \(\frac{1}{2}\)
- D 0
Answer & Solution
Correct Answer
(A) 1
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & y=\log \sqrt{\tan x} \\ & \therefore \quad \frac{d y}{d x}=\frac{1}{\sqrt{\tan x}} \times \frac{1}{2 \sqrt{\tan x}} \times \sec ^2 x=\frac{\sec ^2 x}{2 \tan x} \\ & \therefore \quad\left(\frac{d y}{d x}\right)_{x=\frac{\pi}{4}}=\frac{(\sqrt{2})^2}{2}=1\end{aligned}\)
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