Differentiability
If f(x) = eˣ, then f'(x) equals
Select the correct option:
Solution
eˣ
- Natural Exponential Property: The function ex is the unique non-zero function which is its own derivative.
- Proof Sketch: Using the limit definition f′(x)=limh→0hex+h−ex=exlimh→0heh−1.
- Standard Limit: The limit limh→0heh−1=1.
- Result: f′(x)=ex⋅1=ex.
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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 ex is the unique non-zero function which is its own derivative.
- Proof Sketch: Using the limit definition f′(x)=limh→0hex+h−ex=exlimh→0heh−1.
- Standard Limit: The limit limh→0heh−1=1.
- Result: f′(x)=ex⋅1=ex.
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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