# Partial Derivatives Higher Order

An overview of the second partial derivative, the symmetry of mixed partial derivatives, and higher-order partial derivatives.

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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

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Mixed Partial Derivatives

Subtopic 1

Function more than three variable

Subtopic 1

Other

Figure of Mixed Partial Derivatives

Subtopic 1