Derivatives of Various Functions
Polynomial Derivatives
Trig Derivatives
Inverse Trig Derivatives
Exponential and Logarithmic Derivatives
Beyond Calculus
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Pre-Calculus
- Linear Equations
- Solving Polynomial Equations
- Functions and Domain
- Piecewise Functions
- Topics in Trigonometry
- Exponentials and Logarithms
Limits and Continuity
- The Three Tiers of Limits
- Properties of Limits
- Continuity
- Intermediate Value Theorem
- Limits to Infinity
- Analyzing Functions using Limits
Derivatives
- Definition of the Derivative
- Tanget Lines / Normal Lines
- Differentiability
- Power Rule
- Different Derivatives
- Product Rule
- Quotient Rule
- Chain Rule
- Implicit Differentiation
- Derivatives of Inverse Functions
- Derivatives and Physics
Applications of Derivatives
- Rates of Change
- Increasing / Decreasing
- Maxima and Minima
- First Derivative Analysis
- Concavity and Inflection Points
- First and Second Derivative Analysis
- Graphical Interpretations
- Mean Value Theorem
- Optimization
- Related Rates
- Linearization
- L'Hospital's Rule
Integrals
- Estimating the Integral Using
- Definition of the Integral
- Integration Using Geometry
- Anti-Derivatives
- Definite Integrals
- Average Value of a Function
- Fundamental Theorem of Calculus
- Integration by Substitution
- Slope Fields
- Initial Value Problems
- Differential Equations
Applications of Integrals
- Exponential Growth and Decay
- Net Change
- Integrals and Physics
- Areas Between Curves
- Volumes of Solids Given a Base and Cross Sections
- Solids by Revolution:
Beyond Calculus is designed for students currently taking Calculus.