2. Basic Derivatives The Math Center Tutorial Services Brought To You By:

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

4. 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

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

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

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

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

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

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

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

12. Questions???

13. Helpful Links ► Derivatives and Integrals Handout Derivatives and Integrals Handout Derivatives and Integrals Handout ► Implicit Differentiation Handout Implicit Differentiation Handout Implicit Differentiation Handout ► Derivatives Student Handout Derivatives Student Handout Derivatives Student Handout ► Derivatives Quiz Derivatives Quiz Derivatives Quiz