# Solutions to Problem Set 17

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

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