The derivative of a function is the limit of the slope of the secant line between two points as the distance between the two points approaches 0 and the Instantaneous Rate of Change at a point.

If the derivative has the same domain as the function, the function is differentiable or has a derivative on that domain.

A function may not be differentiable if there is a corner, cusp, or vertical tangent. Also, the function is not differentiable if it is a step function.

(Examples Below)



Limit Definition of the Derivative

Here are the major rules that you will use to take the derivative of any function.

Here are some derivatives that need to be memorized before the AP exam.

Practice Problems

Harder Practice Problems Worked Through

Please visit these other sites to view some of the uses of derivatives.
Particle Motion
Related Rates

Additional Practice problems
Use your book... :)

External Resources
Calculus Tutorials and Problems
Derivative Rules .pdf
Calculus Rules for Derivatives
Derivative Help
Derivative Rules Summary
For additional help:
Google Derivative Rules or Derivative Problems with Calculus