Calculus Formula Sheet:
From Limits to Series
The definitive guide for AP Calculus AB/BC and Engineering Math. Search over 100+ identities, derivatives, and integration rules. Accurate, printable, and completely free.
Limits & Continuity
Applies when limits result in 0/0 or ∞/∞ indeterminate forms.
Essential for deriving derivatives of sine and cosine.
The definition of the base of the natural logarithm (e ≈ 2.718).
Differentiation Rules
Crucial for differentiating functions within functions.
Method for the derivative of a product of two functions.
Common in engineering and integration by substitution.
The unique function that is its own derivative.
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Integration Techniques
The integral equivalent of the product rule for derivatives.
Used to solve integrals involving square roots of quadratic forms.
Breaking complex rational functions into simpler fractions.
Power Series & Taylor
Approximating functions as infinite polynomials centered at a.
The Maclaurin series expansion for the sine function.
The Ultimate Calculus Cheat Sheet for Students
Calculus is the study of continuous change. Whether you are preparing for the AP Calculus exam or studying engineering at university, having a reliable source for Differentiation and Integration formulas is key to your success. Our comprehensive reference sheet is updated for 2026 to include everything from foundational limits to advanced Taylor series expansions.
How to Use This Reference Successfully
Don’t just memorize — understand the relationships. For example, every integration rule on this page is effectively the “inverse” of a differentiation rule. When you see the derivative of ln(x) is 1/x, you immediately know that the integral of 1/x must involve ln(x).
- Limits: Master L’Hôpital’s Rule early. It is the most powerful tool for solving indeterminate forms on exams.
- Derivatives: Focus on the Chain Rule. Over 70% of differentiation errors in exams come from forgetting to multiply by the inner function’s derivative.
- Integrals: Memorize the common trigonometric integrals. While substitution (U-Sub) is common, recognizing the form of arctan or arcsin can save you minutes during a timed test.
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