Calculus Cheat Sheet
Your complete reference for differential and integral calculus. From limits and derivatives to integration techniques and applications — everything you need for university calculus.
Limits
1 topics
Derivatives
10 topics
Definition of the Derivative
The derivative as a limit, instantaneous rate of change, and tangent line slope.
Basic Differentiation Rules
Power rule, constant rule, sum and difference rules for derivatives.
Product and Quotient Rules
Rules for differentiating products and quotients of functions.
Chain Rule
Differentiating composite functions using the chain rule.
Derivatives of Trigonometric Functions
Derivatives of sine, cosine, tangent, and other trigonometric functions.
Derivatives of Exponential and Logarithmic Functions
Derivatives of exponential functions, natural logarithm, and general logarithms.
Derivatives of Inverse Trigonometric Functions
Derivatives of arcsin, arccos, arctan, and other inverse trig functions.
Implicit Differentiation
Finding derivatives when the function is defined implicitly.
Logarithmic Differentiation
Using logarithms to simplify differentiation of complex expressions.
Higher Order Derivatives
Second derivatives, third derivatives, and the nth derivative.
Derivative Applications
6 topics
Related Rates
Solving problems where multiple quantities change with respect to time.
L'Hôpital's Rule
Evaluating limits of indeterminate forms using derivatives.
Mean Value Theorem
The relationship between average and instantaneous rates of change.
Critical Points and Extrema
Finding local and absolute maxima and minima using derivatives.
Curve Sketching
Analyzing functions using derivatives to sketch accurate graphs.
Optimization Problems
Using derivatives to find optimal solutions in applied problems.
Integration Basics
4 topics
Antiderivatives and Indefinite Integrals
Finding functions whose derivative is a given function.
Basic Integration Rules
Power rule, constant multiple rule, and sum rule for integrals.
Definite Integrals
Computing definite integrals and their properties.
Fundamental Theorem of Calculus
The connection between differentiation and integration.
Integration Techniques
5 topics
Integration by Substitution
The u-substitution method for evaluating integrals.
Integration by Parts
Integrating products of functions using the parts formula.
Trigonometric Integrals
Techniques for integrating powers and products of trig functions.
Trigonometric Substitution
Using trig substitutions to evaluate integrals with radicals.
Partial Fractions
Decomposing rational functions for easier integration.
Applications of Integration
6 topics
Improper Integrals
Evaluating integrals with infinite limits or discontinuities.
Area Between Curves
Computing areas enclosed by two or more curves.
Volumes of Revolution (Disk/Washer)
Finding volumes using the disk and washer methods.
Volumes of Revolution (Shell Method)
Finding volumes using the cylindrical shell method.
Arc Length
Computing the length of curves using integration.
Surface Area of Revolution
Finding surface areas of solids of revolution.
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