Math 311-01/02

2-22-2018

* [Partial derivatives problems]*

1. Let . Compute the partial derivatives and .

2. Let . Compute the partial derivatives and .

3. Let . Compute the partial derivatives and .

Use the Product Rule to compute :

4. Let . Compute the partial derivatives , , and .

You can write the function as

Then

5. Let . Compute the partial derivatives , , and .

6. Let . Compute the partial derivatives , , and .

7. Let . Compute the partial derivatives and .

8. Let . Find all points such that and .

Setting and gives

The first equation gives

Plugging this into the second equation gives

Thus, . The point where and is .

*Today is the tomorrow you worried about yesterday. Now you know
why.* - *Anonymous*

Copyright 2018 by Bruce Ikenaga