if z = xy / (x-y), show that x² (∂ ²z / ∂x²) + 2xy (∂ ²z / ∂x∂y) + y² (∂ ²z / ∂y²) = 0

.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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