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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.

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📐Precalculus & Calculus Trig

Trigonometric Identities & Unit Circle Formula Sheet

Every high-yield trigonometric identity for Precalculus, Calculus II trig integrals, and Physics vectors—organized with exam traps and 1-click self-test mode.

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⚡Kinematics, Forces, Energy & Circuits

Physics Equations Sheet: Kinematics, Forces & Energy

Find the exact kinematics, dynamics, energy, or electricity equation you need based on which variable is missing in your physics problem.

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🧪Gen Chem, Acids/Bases & Thermo

Chemistry Formula Sheet: Stoichiometry, Gas Laws & pH

All essential General and AP/University Chemistry equations for stoichiometry, ideal gases, acid-base buffers, thermodynamics, and electrochemistry.

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📊AP Stats, Psych & Biostats

Statistics Formula Sheet: Z-Score, t-Test & Confidence Intervals

Every high-yield statistics and probability formula for AP Statistics, Quantitative Methods (QM), Psychology Research, and Biostatistics.

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💼Finance, Accounting & Microecon

Finance, Accounting & Microeconomics Formula Sheet

Essential corporate finance, financial accounting, and microeconomics equations for business majors, CPA/CFA prep, and MBA core courses.

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Live Preview: Calculus Formulas

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Power Rule (Derivatives)

d/dx [xⁿ] = n · xⁿ⁻¹

When to use: Differentiating polynomials, roots (x¹/²), and negative exponents (1/xⁿ = x⁻ⁿ).

⚠️ Exam Trap: Do not use Power Rule when x is in the exponent (like 2ˣ); use d/dx[aˣ] = aˣ ln(a).

Product Rule

d/dx [f(x)g(x)] = f'(x)g(x) + f(x)g'(x)

When to use: Differentiating two multiplied functions of x (e.g., x² · sin(x)).

⚠️ Exam Trap: Never just multiply the two derivatives together: (fg)' ≠ f'g'.

Quotient Rule

d/dx [f(x)/g(x)] = [f'(x)g(x) - f(x)g'(x)] / [g(x)]²

When to use: Differentiating rational expressions or fractions of x.

⚠️ Exam Trap: Order in the numerator matters because of the minus sign: Low·d(High) - High·d(Low).

Chain Rule

d/dx [f(g(x))] = f'(g(x)) · g'(x)

When to use: Differentiating composite functions like sin(3x²) or (2x + 1)⁵.

⚠️ Exam Trap: Forgetting to multiply by the inside derivative g'(x) is the #1 AP Calculus error.