1. Mr. Jonathan Anderson MAT – 1710 Calculus & Analytic Geometry I SUNY JCC Jamestown, NY

2. Vocab and Notation  The process of finding the derivative of a function is called differentiation.  To differentiate is to find the derivative.  4 different notations:

3. Continuity  Differentiability implies continuity.  Continuity does not imply differentiability (sharp point).  A function is differentiable at a point (x = c) iff a single tangent line to the curve can be drawn at that point.

4. Limit Definition

5. Example

6. Constant Rule  The derivative of a constant is zero.  Example:

7. Power Rule

8. Sum / Difference  The derivative of a sum/difference is the sum/difference of the derivatives.

9. Sine and Cosine

10. The Exponential Function

11. Application to Slope  If you evaluate the first derivative at x=c, that will be the slope of f(x) at x=c.  Therefore, the first derivative of a given function is the function that is collection of points representing the slopes of the given function.

12. Example

13. Homework  Pg. 136 # 3-23 [5], 33-49 EOO, 56, 59-61