Higher order partial derivatives
Multivariable and vector calculus · Mathematics
Study notes
Q: For f(x,y) = x^3 y^2, find fxx, fyy, fxy, fyx. fx = 3x^2 y^2, fy = 2x^3 y. fxx = 6x y^2. fyy = 2x^3. fxy = (fx)_y = 6x^2 y. fyx = (fy)_x = 6x^2 y. Equal, as Clairaut promises!