Question

If \( y = 2^x \), then \[ \frac{dy}{dx} \, \text{at} \, x = e \, \text{is} \]

• A. \( 2 \log 2 \)
• B. \( 2 \log e \)
• C. \( \log 2 \)
• D. 0

Hint:

To differentiate exponential functions with bases other than \( e \), use the chain rule with \( \log \) of the base.

Answer 1

The Correct Option is C

For the given function \( y = 2^x \), the derivative with respect to \( x \) is \( \frac{dy}{dx} = 2^x \log 2 \). At \( x = e \), the derivative is \( \log 2 \).
Step 2: Conclusion.
The correct answer is (C), \( \log 2 \).