Differentiability
Easymathematics
The derivative of f(x) = x³ is
Select the correct option:
Solution
Incorrect! Answer:
3x²
- Power Rule: For any function f(x)=xn, the derivative is f′(x)=nxn−1.
- Substitution: Here n=3.
- Calculation: f′(x)=3⋅x3−1=3x2.
- Geometrically, this represents the slope of the tangent to the curve y=x3 at any point x.
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About This Question
- Subject
- mathematics
- Chapter
- limit, continuity and differentiability
- Topic
- differentiability
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
3x²
- Power Rule: For any function f(x)=xn, the derivative is f′(x)=nxn−1.
- Substitution: Here n=3.
- Calculation: f′(x)=3⋅x3−1=3x2.
- Geometrically, this represents the slope of the tangent to the curve y=x3 at any point 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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