e^x-xyz=0,求∂^2z/∂x^2课本答案是(2y^2ze^x-2xy^3z-y^2z^2e^x)/(e^x-xy)^3，我感觉不对诶

Question

e^x-xyz=0,求∂^2z/∂x^2
课本答案是(2y^2ze^x-2xy^3z-y^2z^2e^x)/(e^x-xy)^3，我感觉不对诶

Answer 1

e^xdx = xydz + xzdy + yzdx (e^x - yz)dx - xzdy = xydz dz = (e^x - yz)/xy * dx - z/y * dy 则∂z/∂x = (e^x - yz)/xy ∂²z/∂x² = ∂(∂z/∂x)/∂x = ͦ...