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Extended Only Algebra and Graphs

The Power Rule for IGCSE Maths

Differentiating terms of the form ax^n. This subtopic is part of Differentiation in the Cambridge IGCSE Mathematics 0580 syllabus (Extended tier only). Understanding the power rule is essential for ac

What You Need to Know

Differentiating terms of the form ax^n. This subtopic is part of Differentiation in the Cambridge IGCSE Mathematics 0580 syllabus (Extended tier only). Understanding the power rule is essential for achieving a strong grade in your IGCSE Maths exam.

Understanding The Power Rule

Differentiation by the power rule: if y = xⁿ, then dy/dx = nxⁿ⁻¹. Multiply by the power, then decrease the power by 1. For polynomials, differentiate term by term. Constants disappear (derivative of a constant = 0). This is the foundation of all differentiation in IGCSE Extended, tested in Paper 4 as a standalone skill and as part of gradient, tangent, normal, and optimisation questions.

Step-by-Step Method

  1. 1

    Identify each term

    Write out each term in the form axⁿ. Rewrite negative indices (e.g. 1/x = x⁻¹) and fractional powers (√x = x^(1/2)) if present.

  2. 2

    Apply the power rule to each term

    For axⁿ: multiply by the power, decrease the power by 1. Result: naxⁿ⁻¹.

  3. 3

    Differentiate constants

    The derivative of any constant is 0. Drop the constant term entirely.

  4. 4

    Simplify

    Collect and simplify the expression. Rewrite negative indices in fraction form if the question requires it.

  5. 5

    Write dy/dx = ...

    Label the derivative as dy/dx (or f'(x) if the function is written as f(x)).

Worked Example

Question

Find dy/dx when y = 4x³ − 3x² + 7x − 5.

Solution

Differentiate term by term: 4x³ → 3 × 4x² = 12x² −3x² → 2 × (−3)x = −6x 7x → 7x⁰ = 7 −5 → 0 (constant) dy/dx = 12x² − 6x + 7 Answer: dy/dx = 12x² − 6x + 7

Exam Tips for The Power Rule

  • Multiply by the original power FIRST, then subtract 1 from the power — not the other way round.
  • Never forget: the derivative of a constant is 0, and the constant disappears entirely from dy/dx.
  • Rewrite surds and fractions as powers before differentiating: √x = x^(1/2), 1/x³ = x⁻³.
  • dy/dx and f'(x) mean the same thing — use whichever notation matches the question.

Practice Questions

Q1: Find f'(x) when f(x) = 5x⁴ − 2x³ + x − 8.

Show hint

f'(x) = 20x³ − 6x² + 1.

Q2: Find dy/dx when y = 3√x + 4/x².

Show hint

Rewrite: y = 3x^(1/2) + 4x⁻². Differentiate: dy/dx = (3/2)x^(−1/2) − 8x⁻³.

Q3: y = (x + 2)(x − 3). Find dy/dx without expanding first, then verify by expanding.

Show hint

Expand: y = x²−x−6. dy/dx = 2x−1. Or use product rule (not in IGCSE syllabus — expand first).

Frequently Asked Questions

What is the power rule in IGCSE Maths?

Differentiating terms of the form ax^n.

Is the power rule in the Core or Extended syllabus?

The Power Rule is part of the Extended only syllabus for IGCSE Mathematics 0580.

How do I revise the power rule effectively?

Start with the revision notes to understand key concepts, then work through the worked examples step by step. Finally, practise past paper questions under timed conditions. Teacher Rig recommends spending focused revision sessions on the power rule rather than trying to cover everything at once.

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