
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 $x$.
• 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.