## Derivatives, Properties, and Formulas

Read this section to understand the properties of derivatives. Work through practice problems 1-11.

The derivative of a function is a new function which gives the slope of the line tangent to the graph of at each point . To find the slope of the tangent line at a particular point on the graph of , we should first calculate the derivative and then evaluate the function at the point to get the number . If you mistakenly evaluate first, you get a number , and the derivative of a constant is always equal to 0.

**Example 10:** Determine the slope of the line tangent to at and :

Solution: When , the graph of goes through the point with slope . When , the graph goes through the point with slope .