Differentiability

Easymathematics

If f(x) = eˣ, then f'(x) equals

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eˣ

xeˣ⁻¹

eˣ/x

ln(x)

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About This Question

Subject: mathematics
Chapter: limit, continuity and differentiability
Topic: differentiability
Difficulty: Easy
Year: 2025

Solution

Correct Answer:

eˣ

Natural Exponential Property: The function $e^{x}$ is the unique non-zero function which is its own derivative.
Proof Sketch: Using the limit definition $f^{'} (x) = lim_{h \to 0} \frac{e ^{x + h} - e ^{x}}{h} = e^{x} lim_{h \to 0} \frac{e ^{h} - 1}{h}$ .
Standard Limit: The limit $lim_{h \to 0} \frac{e ^{h} - 1}{h} = 1$ .
Result: $f^{'} (x) = e^{x} \cdot 1 = e^{x}$ .

This easy difficulty mathematics question is from the chapter limit, continuity and differentiability, covering the topic of differentiability. It appeared in the 2025 exam.

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