Review- 6 Differentiation Rules Derivatives This template can be used as a starter file for presenting training materials in a group setting. Sections Right-click on a slide to add sections. Sections can help to organize your slides or facilitate collaboration between multiple authors. Notes Use the Notes section for delivery notes or to provide additional details for the audience. View these notes in Presentation View during your presentation. Keep in mind the font size (important for accessibility, visibility, videotaping, and online production) Coordinated colors Pay particular attention to the graphs, charts, and text boxes. Consider that attendees will print in black and white or grayscale. Run a test print to make sure your colors work when printed in pure black and white and grayscale. Graphics, tables, and graphs Keep it simple: If possible, use consistent, non-distracting styles and colors. Label all graphs and tables. Review- 6 Differentiation Rules

Definition of the Derivative For a function f(x) the instantaneous rate of change along the function is given by: Which is called the derivative of f Notation:

3) find the Derivative of cos x

Trig Derivatives

The Power Rule If n is a rational number, then the function is differential and 5

4) Find the derivative

The Sum and Difference Rule The derivative of a sum is the sum of the derivatives Proof pg 111

5) Find the derivative

The Product Rule The product of two differentiable functions f and g is itself differentiable. Moreover, the derivative of fg is the first times the derivative of the second, plus the second times the derivative of the first (fg) '(x) = f(x) g '(x) + g(x) f '(x) Proof pg 119

6) Find the derivative

The Quotient Rule The derivative of f  g is given by: The denominator times the derivative of the numerator minus the numerator times the derivative of the denominator all divided by the denominator squared Proof pg 121

7) Find the derivative

The Chain Rule If g(x) is differentiable then Power rule times the derivative of inside Proof pg 131

8) Find the derivative

9) Find the derivative

Home Work Page 158 # 15-29 odd, 41, 45, 49, and 51, and Worksheet 6-B Use a section header for each of the topics, so there is a clear transition to the audience. Page 158 # 15-29 odd, 41, 45, 49, and 51, and Worksheet 6-B