1. Partial Derivatives
Mr. Gammelgaard’s Coffee Break

2. Limit Definition
Leibniz Notation:

3. Higher Order Partial Derivatives
Clairaut’s Theorem: Suppose that f is defined on a disk D that contains the point. If the functions ƒxy(a, b)
and ƒyx(a, b) are continuous on this disk then, ƒxy(a, b) = ƒyx(a, b).

4. Chain Rule
For z = f(x, y), x = g(t), and y = h(t)...

5. Directional Derivatives

6. Problems
Find ƒxy(x, y) where f(x, y) = -8arctan(xy) + e5ycos(x).
Find the directional derivative of f(x, y) = 12cosy(x) - xln(y) where is the unit
vector in the direction of θ = π/3.

7. Solutions

8. Sources
http://tutorial.math.lamar.edu/Classes/CalcIII/
PartialDerivsIntro.aspx
http://en.wikipedia.org/wiki/Partial_derivative