Pages similar to: Exploring the derivative of the exponential function
- The idea of the derivative of a function
The derivative of a function as the slope of the tangent line. - Derivatives of polynomials
How to compute the derivative of a polynomial. - Derivatives of more general power functions
How to compute the derivative of power functions. - A refresher on the quotient rule
How to compute the derivative of a quotient. - A refresher on the product rule
How to compute the derivative of a product. - A refresher on the chain rule
How to compute the derivative of a composition of functions. - Related rates
Calculating one derivative in terms of another derivative. - Intermediate Value Theorem, location of roots
Using the Intermediate Value Theorem to find small intervals where a function must have a root. - Newton's Method
A method to approximate the roots to an equation. - Derivatives of transcendental functions
A list of formulas for taking derivatives of exponential, logarithm, trigonometric, and inverse trigonometric functions. - L'Hospital's rule
A way to simplify evaluation of limits when the limit is an indeterminate form. - The second and higher derivatives
Taking derivatives multiple times to calculate the second or higer derivative. - Inflection points, concavity upward and downward
Finding points where the second derivative changes sign. - Approximating a nonlinear function by a linear function
The secant line and tangent line are two ways to approximate a nonlinear function by a linear one. - Developing intuition about the derivative
An intuitive exploration into the properties of the derivative, illustrated by interactive graphics. - The idea of the chain rule
An illustration of the basic concept of the chain rule using interactive graphics to diagram the relevant points on the graphs and the corresponding slopes. - Simple examples of using the chain rule
Basic examples that show how to use the chain rule to calculate the derivative of the composition of functions. - The derivative of the natural logarithm
Determining the derivative of the natural logarithm from the fact that it is the inverse of the exponential function. - The derivative of an inverse function
How to write the derivative of an inverse function in terms of the derivative of the original function. - Elementary derivative problems
Sample problems illustrating the ordinary derivative.