Free interactive tutorials that may be used to explore a new topic or as a complement to what have been studied already. The analytical tutorials may be used to further develop your skills in solving problems in calculus. Topics in calculus are explored interactively, using large window java applets, and analytically with examples and detailed solutions. Calculus problems are also included in this website. Mutlivariable Functions and partial derivatives are included.
Limits and Continuity
Differentiation and Derivatives
- Find Derivatives of Functions in Calculus. Find the derivatives of various functions using different methods and rules. Several Examples with detailed solutions are presented. Also exercises with answers are included at the end of the page.
- Difference Quotient. We start with the definition of the difference quotient and then use several examples to calculate it. Detailed solutions to questions are presented.
- Use Definiton to Find Derivative. The derivative is found using its definition. The difference quotient is first calculated then its limit computed as h ---> 0.
- Logarithmic Differentiation. A powerful method to find the derivative of complicated functions. The method uses the chain rule and the properties of logarithms.
- Table of Derivatives. A table of derivatives of exponential and logarithmic functions, trigonometric functions and their inverses, hyperbolic functions and their inverses.
- Rules of Differentiation of Functions in Calculus. The basic rules of differentiation of functions in calculus are presented along with several examples.
- Use the Chain Rule of Differentiation in Calculus. The chain rule of differentiation of functions in calculus is presented along with several examples.
- Derivatives Involving Absolute Value. Examples on how to find the derivative of functions involving absolute value. Exercises with answers are also included.
- Implicit Differentiation. Implicit differentiation examples, with detailed solutions, are presented.
- Derivative of Inverse Function. Examples with detailed solutions on how to find the derivative of an inverse function are presented.
- Derivative of Inverse Trigonometric Functions. Formulas of the derivatives of inverse trigonometric functions are presented along with several other examples involving sums, products and quotients of functions.
- Find Derivative of f(x) = arccos(cos(x)) and graph it.
- Find Derivative of f(x) = arcsin(sin(x)) and graph it.
- Find Derivative of f(x) = arctan(tan(x)) and graph it.
- Differentiation of Trigonometric Functions. Formulas of the derivatives of trigonometric functions, in calculus, are presented along with several examples involving products, sums and quotients of trigonometric functions.
- Find Derivative of y = xx. A tutorial on how to find the first derivative of y = xx for x > 0.
- Differentiation of Exponential Functions. Formulas and examples of the derivatives of exponential functions, in calculus, are presented. Several examples, with detailed solutions, involving products, sums and quotients of exponential functions are examined.
- Differentiation of Logarithmic Functions. Examples of the derivatives of logarithmic functions, in calculus, are presented. Several examples, with detailed solutions, involving products, sums and quotients of exponential functions are examined.
- Differentiation of Hyperbolic Functions. A table of the derivatives of the hyperbolic functions is presented. Examples, with detailed solutions, involving products, sums, power and quotients of hyprbolic functions are examined.
Application of Differentiation
Multivariable Functions (Functions with several variables)
Tables of Mathematical Formulas
- Tables of Mathematical Formulas. Several tables of mathematical formulas including decimal multipliers, series, factorial, permutations, combinations, binomial expansion, trigonometric formulas and tables of derivatives, integrals, Laplace and Fourier transforms.