Product, quotient & chain rules
Practice Flashcards
Flip to reveal answersState the chain rule.
Track your progress — Sign up free to save your progress and get smart review reminders based on spaced repetition.
All 8 Flashcards — Product, quotient & chain rules
Sign up free to track progress and get spaced-repetition review schedules.
Question
State the chain rule.
Answer
dy/dx = dy/du · du/dx — differentiate the outer function, then multiply by the derivative of the inside.
Question
d/dx of e^{kx}?
Answer
k·e^{kx} (chain rule: the k is the derivative of the inside kx).
Question
d/dx of (ax + b)ⁿ?
Answer
n·a·(ax + b)^(n−1) — power rule on the outside, times a (the inside derivative).
Question
State the product rule.
Answer
(uv)′ = u′v + uv′ — first times derivative of second, plus second times derivative of first.
Question
State the quotient rule.
Answer
(u/v)′ = (u′v − uv′)/v² — mind the minus and the order u′v − uv′.
Question
How do you decide which rule to use?
Answer
Fraction → quotient; two factors multiplied → product; a function inside a function → chain.
Question
Differentiate y = x·eˣ.
Answer
Product rule: (1)eˣ + x·eˣ = eˣ(1 + x).
Question
d/dx of sin(3x)?
Answer
3cos(3x) (chain rule: derivative of the inside 3x is 3).
Read the notes
Full study notes for Product, quotient & chain rules
Topic 5.9 hub
Differentiation rules (HL only)
More from Topic 5.9
All flashcards in this topic
Math AI exam skills
Paper structures & tips
Track your progress with spaced repetition
Sign up free — Aimnova tells you exactly which cards to review and when, so you remember everything before your IB exam.
Start Free