BASIC DIFFERENTIATION RULES AND RATES OF CHANGE

BASIC DIFFERENTIATION RULES AND RATES OF CHANGE PowerPoint PPT Presentation


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BASIC DIFFERENTIATION RULES AND RATES OF CHANGE

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1. BASIC DIFFERENTIATION RULES AND RATES OF CHANGE Section 2.2

2. When you are done with your homework, you should be able to… Find the derivative of a function using the Constant Rule Find the derivative of a function using the Power Rule Find the derivative of a function using the Constant Multiple Rule Find the derivative of a function using the Sum and Difference Rules Find the derivatives of the sine function and the cosine function Use derivatives to find rates of change

3. THE CONSTANT RULE The derivative of a constant function is zero. That is, if c is a real number, then

4. Find the slope of -3 0 undefined

5. -3 0 undefined ?

6. THE POWER RULE If n is a rational number, then the function is differentiable and For f to be differentiable at n must be a number such that is defined on an interval containing 0.

7. Evaluate

8. Evaluate Both A and B

9. THE CONSTANT MULTIPLE RULE If f is a differentiable function and c is a real number, then cf is also differentiable and

10. Evaluate

11. Evaluate the derivative of at 81 -162 -810 -486

12. THE SUM AND DIFFERENCE RULES The sum or difference of two differentiable functions f and g is itself differentiable. The derivative of the sum or difference of functions is the sum or difference of the derivatives of f and g.

13. DERIVATIVES OF SINE AND COSINE FUNCTIONS

14. Evaluate the slope of the graph at 1/2 -1/2

15. RATES OF CHANGE Velocity Average Velocity Instantaneous Velocity

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