Z=X2+Y2 X2+2Y2+3Z2=4 求dy/dx,dz/dx

Z=X2+Y2 ①X2+2Y2+3Z2=4②①两边对x求导,得dz/dx=2x+2ydy/dx③②两边对x求导,得2x+4ydy/dx+6zdz/dx=0④③代入④,得2x+4ydy/dx+6z(2x+2ydy/dx)=0x+2ydy/dx+6z(x+ydy/dx)=0(2y+6yz)dy/dx=-x-6xzdy/dx=(-x-6xz)/(2y+6yz...