Partial Derivatives and the Gradient

1
Partial Derivatives and the Gradient
2
Definition of Partial Derivative
3
Geometric Interpretation
z
Slope fx(x0,y0)
y
(x0,y0)
x
4
Geometric Interpretation
z
Slope fy(x0,y0)
y
(x0,y0)
x
5
Evaluating Partial Derivatives from the
Definition
6
Example
7
Definition of Partial Derivative
8
Leibnizs Notation
9
Example
10
Examples
11
Example
r
h
R
12
Mixed Partials
13
Example
14
Remark
15
Definition of Gradient
16
Example
17
Example
18
Does Partial Differentiability Imply Continuity?
19
Gradient Formulas