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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
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**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