.Let u be a function of x, y , z where x , y, z are independent variables and u depends on x, y ,z..When doing partial differentiation w.r.t x, we treat x alone as the independent variable and treat y and z as constants.
The partial derivative of u with respect to x is usually denoted by ∂u / ∂x
If ∂u / ∂x is again differentiated partially with respect to x we get the partial derivative denoted as ∂ ²u / ∂x²
If ∂u / ∂x is again differentiated partially with respect to y we get the partial derivative denoted as ∂ ²u /∂y ∂x
If ∂u / ∂y is again differentiated partially with respect to x we get the partial derivative denoted as ∂ ²u /∂x ∂y
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