Unlike AP Chemistry or Physics, AP Calculus AB provides no formula sheet. Every derivative, integral, theorem, and limit definition must come from memory. This makes concept mastery non-negotiable.
Essential Derivatives to Know
- d/dx[xⁿ] = nxⁿ⁻¹, d/dx[eˣ] = eˣ, d/dx[ln x] = 1/x
- d/dx[sin x] = cos x, d/dx[cos x] = −sin x, d/dx[tan x] = sec²x
- d/dx[arcsin x] = 1/√(1−x²), d/dx[arctan x] = 1/(1+x²)
- Chain rule, product rule, quotient rule — must apply fluently without hesitation
Essential Integrals to Know
- ∫xⁿ dx = xⁿ⁺¹/(n+1) + C, ∫eˣ dx = eˣ + C, ∫1/x dx = ln|x| + C
- ∫sin x dx = −cos x + C, ∫cos x dx = sin x + C, ∫sec²x dx = tan x + C
- Fundamental Theorem of Calculus (both parts) — appears on virtually every exam
Key Theorems to Know
Mean Value Theorem, Intermediate Value Theorem, Extreme Value Theorem, and L'Hôpital's Rule. For each, know the hypotheses (what conditions must be satisfied) and the conclusion (what it guarantees). FRQ justifications require stating the theorem, not just applying it.
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