设函数u=f(r),r=√(x^2+y^2+z^2),则э^2u/эx^2+э^2u/эy^2+э^2u/эz^2=э^2u/эx_数学解答

设函数u=f(r),r=√(x^2+y^2+z^2),则э^2u/эx^2+э^2u/эy^2+э^2u/эz^2=
э^2u/эx^2代表u对x的二阶偏导数

人气：323 ℃　时间：2020-05-23 22:07:00

解答

эu/эx=f'(r)*эr/эx=f'(r)*x/rэ^2u/эx^2=f''(r)*(x/r)^2+f'(r)*(r-x*x/r)/r^2=f''(r)*(x/r)^2+f'(r)*(r^2-x^2)/r^3同理э^2u/эy^2=f''(r)*(y/r)^2+f'(r)*(r^2-y^2)/r^3э^2u/эz^2=f''(r)*(z/r)^2+f'(r)*(r^2-...