Calculus Derivatives & Integrals Formula Sheet
Master the core differentiation and integration rules tested on Calculus I, Calculus II, CÉGEP NYA/NYB, and AP Calculus AB/BC exams. Toggle Self-Test Mode below to quiz yourself.
High-Yield Formulas
When to use: Differentiating polynomials, roots (x¹/²), and negative exponents (1/xⁿ = x⁻ⁿ).
When to use: Differentiating two multiplied functions of x (e.g., x² · sin(x)).
When to use: Differentiating rational expressions or fractions of x.
When to use: Differentiating composite functions like sin(3x²) or (2x + 1)⁵.
When to use: Evaluating definite integrals and net accumulation of rate of change.
When to use: Integrating products like ∫ x·eˣ dx or ∫ ln(x) dx (choose u via LIATE).
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Frequently Asked Questions
How do I know whether to use u-substitution or Integration by Parts?
Check u-substitution first: if one part of the integrand is the derivative of an inner function (like ∫ 2x·cos(x²) dx), use u-sub. If it is a product of unrelated function families (like ∫ x·eˣ dx), use Integration by Parts.