方法如下,请作参考:
详细:
z = e^(x/y), ∂z/∂x = e^(x/y)/y, ∂z/∂y = -xe^(x/y)/y^2,
∂^2z/∂x∂y = [e^(x/y)(-x/y^2)y-e^(x/y)]/y^2 = -(x+y)e^(x/y)/y^3,
∂^2z/∂y^2 = -x[e^(x/y)(-x/y^2)y^2-e^(x/y)(2y)]/y^4 = x(x+2y)e^(x/y)/y^4.