## Derivatives, Properties, and Formulas

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

**Differentiability and Continuity:** If a function is differentiable then it must be continuous.

If a function is not continuous then it cannot be differentiable.

A function may be continuous at a point and not differentiable there.

**Graphically:** CONTINUOUS means **connected**.

DIFFERENTIABLE means continuous, **smooth **and not vertical.

**Differentiation Patterns:**

The FINAL STEP used to evaluate f indicates the FIRST RULE to use to differentiate .

To evaluate a derivative at a point, first differentiate and then evaluate.