Find the first partial derivatives of f(x, y) = sin(x - y) at the point
(3, 3).

A.

B.

A) 1

B) -1

The work

3.

Find the first partial derivatives of
at the point (x,y) = (3, 4).

0.1633

-0.12245

The work

4.

Find the partial derivatives of the function

The work

5.

Find the first partial derivatives of f(x,y,z) = z ( arctan(y/x) ) at
the point (4, 4, 5).

A.

B.

C.

A) -5/8

B) 5/8

C) 0.7854

The work

6.

The gas law for a fixed mass m of an ideal gas at absolute
temperature T, pressure P, and volume V is PV = mRT,
where R is the gas constant.
Find the partial derivatives

-(mRT)/V^2

mR/P

V/(mR)

-1

The work

7.

Find the partial derivatives of the function
You should as a by product verify that the function f satisfies Clairaut's theorem.