Question

高等数学隐函数

高等数学隐函数求解

Answer 1

yz^2 - xz^3 = 1, z 必不为 0.
2yz∂z/∂x - z^3 - 3xz^2∂z/∂x = 0
∂z/∂x = z^3/(2yz-3xz^2) = z^2/(2y-3xz)
∂^2z/∂x^2 = ∂[z^2/(2y-3xz)]/∂x
= [2z(2z-3xz)∂z/∂x - z^2(-3z-3x∂z/∂x)]/(2y-3xz)^2
= z^2[2(2-3x)∂z/∂x + 3(z+x∂z/∂x)]/(2y-3xz)^2
= z^2[3z+(4-3x)∂z/∂x]/(2y-3xz)^2
= z^2[3z+(4-3x)z^2/(2y-3xz)]/(2y-3xz)^2
= z^3[3(2y-3xz)+(4-3x)z]/(2y-3xz)^3
= 2z^3(3y-6xz+2z)/(2y-3xz)^3