根号下x平方加y平方加z平方分之xyz的偏导数怎么求

Answer 1

u = xyz/√(x²+y²+z²).....................................................(1)
∂u/∂x = [yz√(x²+y²+z²)-xxyz/√(x²+y²+z²)]/(x²+y²+z²)
= yz(y²+z²)/(x²+y²+z²)√(x²+y²+z²).......................(2)
∂u/∂y = xz(x²+z²)/(x²+y²+z²)√(x²+y²+z²).......................(3)
∂u/∂z = xy(y²+x²)/(x²+y²+z²)√(x²+y²+z²).......................(4)