Unit 3: The power rule
About this unit
Expanding (x + h)ⁿ shows that only the term with a single h survives, so the derivative of xⁿ is n·xⁿ⁻¹, and it works term by term for sums, multiples, roots and reciprocals.
By the end, you can: Derive the power rule by expanding (x + h)ⁿ, then use it with sums, constant multiples, 1/x and √x to find derivatives and slopes.
Modules
5 modulesLearn
- Where n·xⁿ⁻¹ comes fromArticle · Expand (x + h)² and (x + h)³: terms with two or more h's vanish after dividing by h, leaving n·xⁿ⁻¹; the rule extends to 1/x and √x, sums and multiples.Not started
- A polynomial, term by termWalkthrough · Differentiate 4x³ − 5x² + 7x − 2 term by term and find its slope at x = 1.Not started
- Roots and reciprocalsWalkthrough · Rewrite 6√x + 2/x as powers, differentiate, and find the slope at x = 4.Not started
- The rule in one placeReview · Bring the power down, lower it by one; rewrite roots and fractions as powers; go term by term.Not started