偏微分基本问题Letf:R2---Rbedi\x0berentiableat(0;0),andforeveryrealnumberx,f(x;-x)=0andf(x;x)=2x.Find偏微分xf(0;0)and偏微分yf(0;0).Hint:Usethefactthat(0;0)belongstoboththelinesx=yandx=-y.

Question

偏微分基本问题
Let f :R2 --- R be di\x0berentiable at (0; 0),and for every real number x,
f(x;-x) = 0 and f(x; x) = 2x.Find 偏微分xf(0; 0) and 偏微分yf(0; 0).
Hint:Use the fact that (0; 0) belongs to both the lines x = y and x = -y.

Answer 1

偏微分xf(0; 0) =x趋于零[f(x; x)-f(-x;x)]/2x=1
偏微分yf(0; 0) =x趋于零[f(x; x)-f(x;-x)]/2x=1