Higher-order partial differentiation
Given a multivariate function, say f(x,y), we may partially differentiate it more than once with respect to either variable. If we differentiate f(x,y) w.r.t. x and y, we have f_x(x,y) and f_y(x,y), respectively. If we differentiate them w.r.t. y and x, respectively, we have f_xy(x,y) and f_yx(x,y), respectively. If these second derivatives are continuous, they are equal: f_xy(x,y) = f_yx(x,y).
Lecture notes: https://bruneimathclub.blogspot.com/2...
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