1. Basic Derivatives
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2. Definition Of A Derivative
The derivative of a function at a point x=a, can be interpreted in several different ways:
Algebraically, the
Geometrically as the slope of the tangent line to the graph of at
Functionally as the instantaneous rate of change of at

3. Applications of Derivatives
Finding the instantaneous velocity of an object at a precise moment in time
Finding the instantaneous rate of change of a function
Finding the slope of the tangent to the graph of a function
* NOTE: the derivative symbol can be written as or or

4. Basic Derivative Formulas
Power Rule
If , where n is a constant, then
If , where c is a constant, then
If , where c is a constant, then
Constant Rule
Power Rule

5. More basic derivative formulas
Logarithm Rule
If , then
Exponential Rule
If , then

6. Following the Power Rule,
Examples
Differentiate:
Solution:
Following the Power Rule,
we can now calculate the derivative.

7. Following the Constant Rule, we can now calculate the derivative.
Examples (cont.)
Differentiate:
Solution:
Following the Constant Rule, we can now calculate the derivative.

8. Following the Power Rule, we can now calculate the derivative.
Examples (cont.)
Differentiate:
Solution:
Following the Power Rule, we can now calculate the derivative.

9. Following the Logarithm Rule, we can now calculate the derivative.
Examples (cont.)
Differentiate:
Solution:
Following the Logarithm Rule, we can now calculate the derivative.
u = x
u’ = 1

10. Following the Exponential Rule, we can now calculate the derivative.
Examples (cont.)
Differentiate:
Solution:
Following the Exponential Rule, we can now calculate the derivative.

11. Questions???

12. Helpful Links Derivatives and Integrals Handout
Implicit Differentiation Handout
Derivatives Student Handout
Derivatives Quiz