Question:
If \( y = 2^x \), then
\[
\frac{dy}{dx} \, \text{at} \, x = e \, \text{is}
\]
If \( y = 2^x \), then
\[
\frac{dy}{dx} \, \text{at} \, x = e \, \text{is}
\]
Show Hint
To differentiate exponential functions with bases other than \( e \), use the chain rule with \( \log \) of the base.
Updated On: Jan 12, 2026
- \( 2 \log 2 \)
- \( 2 \log e \)
- \( \log 2 \)
- 0
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The Correct Option is C
Solution and Explanation
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), \( \log 2 \).
Step 2: Conclusion.
The correct answer is (C), \( \log 2 \).
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