TLDR: AP Calculus Formula Sheet

• Covers derivatives, integrals, limits, and series formulas

• Includes AP reference sheet + must-know rules

• One-page printable PDF for quick review

• Reviewed by Ivy-League calculus tutors

• Download link above

Why Formulas Matter for AP Calculus Success

AP Calculus exams test not only your understanding of concepts but also your ability to quickly apply the right formulas under timed conditions. Having a clear, well-organized formula sheet makes practice and test day much smoother. This guide brings together the most important AP Calculus formulas, tips from our tutors, and a free downloadable PDF for study and revision.

Check out our AP Calculus Resource Hub for more AP tips, or explore our SAT Math Formula Sheet and ACT Math Formula Sheet.

Key AP Calculus Formulas

1. Differentiation Formulas

• Power Rule: d/dx [xⁿ] = n·xⁿ⁻¹

• Product Rule: (fg)’ = f’g + fg’

• Quotient Rule: (f/g)’ = (f’g – fg’)/g²

• Chain Rule: d/dx [f(g(x))] = f’(g(x))·g’(x)

• Trig Derivatives:

  • d/dx [sin x] = cos x

  • d/dx [cos x] = –sin x

  • d/dx [tan x] = sec²x

• Exponential & Logarithmic Derivatives:

  • d/dx [e^x] = e^x

  • d/dx [ln x] = 1/x

Tutor Tip💡: Our MIT tutor reminds students that the chain rule is the most frequently tested derivative rule on the AP exam. Make it second nature.

2. Integration Formulas

• Basic Rules:

  • ∫ xⁿ dx = (xⁿ⁺¹)/(n+1) + C, n ≠ –1

  • ∫ e^x dx = e^x + C

  • ∫ 1/x dx = ln|x| + C

• u-Substitution: ∫ f(g(x))·g’(x) dx → ∫ f(u) du

• Integration by Parts: ∫ u dv = uv – ∫ v du

• Trig Integrals (examples):

  • ∫ sin x dx = –cos x + C

  • ∫ cos x dx = sin x + C

  • ∫ sec²x dx = tan x + C

3. Limits & Continuity

• Standard Limit Laws: lim (f(x) + g(x)) = lim f(x) + lim g(x)

• L’Hôpital’s Rule: If lim f(x)/g(x) is 0/0 or ∞/∞, then lim f/g = lim f’/g’

• Continuity: f(x) is continuous at c if lim x→c f(x) = f(c)

4. Sequences & Series (Quick Formulas)

• Geometric Series: Σ arⁿ = a/(1–r), |r| < 1

• Taylor/Maclaurin Expansion: f(x) ≈ f(a) + f’(a)(x–a) + f’’(a)(x–a)²/2! + …

Tutor Insights: How to Use These Formulas Effectively

Our tutors recommend:

• Practice by category: Don’t just memorize. Work through practice questions using the formulas.

• Know when to apply: For example, chain rule is almost always tested with composite functions.

• Watch for traps: In integration, always double-check if u-substitution or parts is more efficient.

• Timed drills: Simulate exam conditions and practice applying formulas quickly.

Next Steps: Get Expert Support

Formulas are the foundation, but true AP Calculus success comes from applying them to challenging problems. Our Ivy League and 5+ scorers specialize in making calculus strategies simple and effective.

👉 Book a free strategy session with North American Tutors today and get personalized AP Calculus prep.