A function e.g f(x,y) or z(x,y)

Taking two consecutive partial derivatives with respect to the same variable

Standard Notation

Taking partial derivatives with respect to one variable, and then take another partial derivative with respect to a different variable

Standard Notation

Del Notation

Subscript Notation

Mixed partial derivatives give same result whenever :

Third and higher order :

Mechanics of Fluid : Ideal Flow

Finite Element Method or Analysis

Mechanics of Materials : Macaulay's Beam Deflection

Second Partial Derivatives

Mixed Partial Derivatives

Function more than three variable

Figure of Mixed Partial Derivatives