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6.Simple Derivative Rules
Class 11 • Mathematics • NCERT
Simple Derivative Rules
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This lesson introduces basic rules of differentiation as prescribed by NCERT Class 11. Students learn simple derivative rules that help differentiate functions easily without using first principles every time.
Lesson Objectives
- Learn basic rules of differentiation.
- Differentiate simple algebraic functions.
- Apply derivative rules correctly.
- Build speed and accuracy.
1. Derivative of a Constant
If f(x) = c, where c is a constant, then:
d/dx (c) = 0
2. Power Rule
If f(x) = xⁿ, where n is a real number, then:
d/dx (xⁿ) = n·xⁿ⁻¹
3. Constant Multiple Rule
If f(x) = k·g(x), where k is a constant, then:
d/dx [k·g(x)] = k·g′(x)
4. Sum and Difference Rule
The derivative of a sum or difference of functions is the sum or difference of their derivatives.
d/dx [f(x) ± g(x)] = f′(x) ± g′(x)
5. Simple NCERT Examples
• d/dx (7) = 0
• d/dx (x³) = 3x²
• d/dx (5x²) = 10x
• d/dx (x² + 3x) = 2x + 3
• d/dx (x³) = 3x²
• d/dx (5x²) = 10x
• d/dx (x² + 3x) = 2x + 3
6. Important NCERT Notes
• Rules save time compared to first principles
• Valid only for differentiable functions
• Used extensively in higher classes
• Valid only for differentiable functions
• Used extensively in higher classes
Practice Questions (NCERT)
- Find d/dx (9).
- Find d/dx (x⁴).
- Find d/dx (3x²).
- Find d/dx (x³ − x).
- Find d/dx (5x − 7).
- State the power rule.
- What is the derivative of a constant?
- Is d/dx (f + g) = f′ + g′?
- Can these rules replace first principles always?
- Is this topic part of NCERT Class 11 syllabus?
✅ Show Answer Key
- 0
- 4x³
- 6x
- 3x² − 1
- 5
- d/dx (xⁿ) = n·xⁿ⁻¹
- Zero
- Yes
- No
- Yes
© Aviate Learning – Limits & Derivatives (NCERT Class 11)