Rules of differentiation modules
Overview
After completing this section, students should be able to do the following.
- Use the definition of the derivative to develop shortcut rules to find the derivatives of constants and constant multiples.
- Use the definition of the derivative to develop shortcut rules to find the derivatives of powers of xx.
- Use the definition of the derivative to develop shortcut rules to find the derivatives of sums and differences of functions.
- Compute the derivative of polynomials.
- Recognize different notation for the derivative.
- State the derivative of the natural exponential function.
- State the derivative of the sine function.
Patterns in derivatives
Ximera Module
Two young mathematicians think about ``short cuts'' for differentiation.
Basic rules of differentiation
Ximera Module
We derive the constant rule, power rule, and sum rule.
The derivative of the natural exponential function
Ximera Module
We derive the derivative of the natural exponential function.
The derivative of sine
Ximera Module
We derive the derivative of sine.