偏导数的概念可以推广到二元以上函数如u= f(x,y,z)在 (x,y,z) 处f(x+ 4x, y,z)- f(x, y,z)f.(x,y,z) = lim4x4x-→>0f(x, y+4y,z) - f(x, y,z)f,(x, y,z) = lim4y4y-→0f(x,y,z+Az)- f(x,y,z)f.(x,y,z) = lim4z4z->0
如 u = f (x, y,z) 在 (x, y,z) 处 , ( , , ) ( , , ) ( , , ) lim 0 x f x x y z f x y z f x y z x x + − = → , ( , , ) ( , , ) ( , , ) lim 0 y f x y y z f x y z f x y z y y + − = → . ( , , ) ( , , ) ( , , ) lim 0 z f x y z z f x y z f x y z z z + − = → 偏导数的概念可以推广到二元以上函数
一般地，设W= f(Xi,X2,..,xn)Owf(x,.",x, + Ax,,..,xn)- f(xi,".,X,,...,xn)=limax;4x;4x;0(i =1,2,......,n)
一般地，设 1 2 ( , , , ) w f x x x = n i i i n i n x i x f x x x x f x x x x w i ( , , , , ) ( , , , , ) lim 1 1 0 + − = → (i = 1,2, ,n)