chapter 1 mathh3 mti unissdsadsadsaddasdasd

math 3

1. Chapter 1   Partial Derivatives   Revision:

2. In this chapter we deal with functions of more than one variable. For example if we deal with function of two variables only EXAMPLE- 1 :     (treating y as a constant)   (treating x as a constant)

3. EXAMPLE - 2: For , compute   Solution: Treating as a constant, we have : Similarly , treating as a constant, we have:  

4. second-order partial derivatives If we have a function of two variables Note:   EXAMPLE - 3: Find all second-order partial derivatives   Solution:

5. EXAMPLE- 4 : For   Solution : we first rewrite as         we treat and as constants   treating and as constants   treating and as constants  

6. EXAMPLE - 5 : If Show that   Solution:     (2)   Multiply (1) by and (2) by we get     Divided by    

7. The Chain Rule ► Case 1 Suppose that       Example 6 :- Suppose that     Use the chain rule to find   Solution    

8. ► Case 2 Suppose that         and Example 7:- If     Find   Solution using chain rule       and      

9. Solve the following very important problem