2-Basic Rules of Differentiation Quotient Rule.pptx

dsfgewffgefr

1. DERIVATIVES BASIC RULES OF DIFFERENTIATION

2. RULE 6: THE QUOTIENT RULE This rule may look overwhelming with the functions but it is easy to learn if you can repeat these words: The derivative of a quotient is the bottom times the derivative of the top minus the top times the derivative of the bottom over the bottom squared .    

3. Expressing quotient rule in terms of function u and v (remember u and v are functions of x):   or        

4. Example of the Quotient Rule: Find   First we will find the derivative by using The Quotient Rule    

5.   Another way to do the same problem is to do the division first and then use the power rule. Again, notice there is more than one method you could use to find the derivative.

6. Example 2: Find the derivative of   For this quotient doing the division first would require polynomial long division and is not going to eliminate the need to use the Quotient Rule. So you will want to just use the Quotient Rule.  

7. DIFFERENTIABLE FUNCTION ARE CONTINUOUS A function is continuous at every point where it has a derivative. Theorem 1 If f has a derivative at x = c , then f is continuous at x = c.

8. Continuous Function may or may not be Differentiable For Example the absolute function, f =|x|, is not differentiable at x = 0,

9. Definition of a derivative at a given point  

10. Higher Order Derivatives:   is the first derivative of y with respect to x.   is the second derivative. (y double prime)   is the third derivative.   is the fourth derivative.

11. Higher Order Derivatives: Find the second and third derivative of the function below:  

12. CONCLUDING REMARKS

13. CONCLUDING REMARKS