Partial Derivatives Higher Order

Partial Derivatives : Higher Order
1. Introduction
A function e.g f(x,y) or z(x,y)
2. Second Partial Derivatives
Taking two consecutive partial derivatives with respect to the same variable
Standard Notation
fxx
fyy
3. Mixed Partial Derivatives
Taking partial derivatives with respect to one variable, and then take another partial derivative with respect to a different variable
Standard Notation
fyx
fxy
Del Notation
Subscript Notation
4. Higher Partial Derivatives
Mixed partial derivatives give same result whenever :
f, fx, fy, fxy, fyx
Third and higher order :
fyyx
fyyxx
Engineering Applications
Mechanics of Fluid : Ideal Flow
Finite Element Method or Analysis
Mechanics of Materials : Macaulay's Beam Deflection
Example Questions
Second Partial Derivatives
Subtopic 1
Mixed Partial Derivatives
Subtopic 1
Function more than three variable
Subtopic 1
Other
Figure of Mixed Partial Derivatives
Subtopic 1
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