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y = sinx, dy/dx = cosx
φ(x^2, e^y, z) = 0, 两边对 x求导,得
2xφ'1+e^y(dy/dx)φ'2+(dz/dx)φ'3 = 0
2xφ'1+e^y cosx φ'2+(dz/dx)φ'3 = 0
得 dz/dx = -(2xφ'1+e^y cosx φ'2)/φ'3.
u = f(x, y, z)
du/dx = f'1+f'2dy/dx+f'3dz/dx
= f'1+f'2cosx-f'3(2xφ'1+e^y cosx φ'2)/φ'3
φ(x^2, e^y, z) = 0, 两边对 x求导,得
2xφ'1+e^y(dy/dx)φ'2+(dz/dx)φ'3 = 0
2xφ'1+e^y cosx φ'2+(dz/dx)φ'3 = 0
得 dz/dx = -(2xφ'1+e^y cosx φ'2)/φ'3.
u = f(x, y, z)
du/dx = f'1+f'2dy/dx+f'3dz/dx
= f'1+f'2cosx-f'3(2xφ'1+e^y cosx φ'2)/φ'3
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