← MATH 01130 · Calculus I
MATH 01130 · Derivatives
Power, product, quotient, chain rules
Definition
Power: (xⁿ)′=n xⁿ⁻¹. Product: (uv)′=u′v+uv′. Quotient: (u/v)′=(u′v−uv′)/v². Chain: (f(g(x)))′=f′(g(x))·g′(x).
Read this
Chain rule is the #1 Calc I skill: always ask “outside derivative × inside derivative.”
Memorize derivatives of sin, cos, tan, eˣ, ln|x|, and aˣ. Combine with the four rules.
Check with a quick expand for simple cases (e.g. (x²·x³)′ should match (x⁵)′).
Drill with flashcards
Flip through these until you can say the answer before revealing it.
Flashcards · 1 / 4
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Try this
Attempt each problem first, then open the worked solution.
1.Differentiate (3x²+1)⁵ sin(2x) with product+chain.