一元二重复合函数求导法则（B012）

问题

设函数 $z$ $=$ $f(u, v)$, $u$ $=$ $\varphi(x)$, $v$ $=$ $\psi(x)$, 则 $\frac{\mathrm{d} z}{\mathrm{d} x}$ $=$ $?$

选项

[A]. $\frac{\mathrm{d} z}{\mathrm{~d} x}$ $=$ $\frac{\partial z}{\partial u}$ $\cdot$ $\frac{\mathrm{d} u}{\mathrm{d} x}$ $\cdot$ $\frac{\partial z}{\partial v}$ $\cdot$ $\frac{\mathrm{d} v}{\mathrm{d} x}$

[B]. $\frac{\mathrm{d} z}{\mathrm{~d} x}$ $=$ $\frac{\partial z}{\partial u}$ $\cdot$ $\frac{\mathrm{d} u}{\mathrm{d} x}$ $+$ $\frac{\partial z}{\partial v}$ $\cdot$ $\frac{\mathrm{d} v}{\mathrm{d} x}$

[C]. $\frac{\mathrm{d} z}{\mathrm{~d} x}$ $=$ $\frac{\partial z}{\partial u}$ $\cdot$ $\frac{\partial u}{\partial x}$ $+$ $\frac{\partial z}{\partial v}$ $\cdot$ $\frac{\partial v}{\partial x}$

[D]. $\frac{\mathrm{d} z}{\mathrm{~d} x}$ $=$ $\frac{\partial z}{\partial u}$ $+$ $\frac{\partial z}{\partial v}$

答案

$\frac{\mathrm{d} z}{\mathrm{~d} x}$ $=$ $\frac{\partial z}{\partial u}$ $\cdot$ $\frac{\mathrm{d} u}{\mathrm{d} x}$ $+$ $\frac{\partial z}{\partial v}$ $\cdot$ $\frac{\mathrm{d} v}{\mathrm{d} x}$

问题

选项

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