设z=arctany/x,则z关于y的二阶偏导数是?
问题描述：
设z=arctany/x,则z关于y的二阶偏导数是?
答
z=arctany/x
δz/δy = 1/[1+(y/x)^2] * [1/x] = x/[x^2+y^2]
δ²z/δy² =δ(δz/δy)/δy = -x(2y)/[x^2+y^2]^2 = -2xy/[x^2+y^2]^2