Question

If \(y = sin(e^{log2x})\), then the value of \(\frac{dy}{dx}\) at \(x = \frac{π}{2}\) is

• A. \(2\)
• B. \(-2\)
• C. \(1\)
• D. \(-1\)

Hint:

Use $e^{\log a}=a$ to simplify before differentiating.

Answer 1

The Correct Option is B

Step 1: Simplify
\(e^{\log2x}=2x\), so \(y=\sin2x\).

Step 2: Differentiate
\(\frac{dy}{dx}=2\cos2x\).

Step 3: Evaluate
At \(x=\frac{\pi}{2}\): \(2\cos\pi=-2\). Option (B).

Final Answer:
\(\frac{dy}{dx}=-2\), option (B). \[ \boxed{\text{(B) } -2} \]