Find http://ppt.cc/u-r- by using implicit function theorem
f(x,y,z)=sinx+y*cosx-x*y*z-10=0
(f_x,f_y,f_z)=(cosx-y*sinx-y*z,cosx-x*z,x*y)....(*)
If x*y=0 then x=0 or y=0
Case 1 x=0 y≠0
(*)代x=0 y≠0 得(1-y*z,1,0)≠(0,0,0)
Case 2 x≠0 y=0
(*)代x≠0 y=0 得(cosx,cosx-x*z,0)≠(0,0,0)
Case 3 x=0 y=0
(*)代x=0 y=0 得(1,1,0)≠(0,0,0)
所以(f_x,f_y,f_z)≠(0,0,0)
f satisfies Implicit Function Thm
請問接下來怎麼解 謝謝