链式法则

Derivative Rules

Rules	Function	Derivative
sum	$f+g$	$f^{'}+g^{'}$
difference	$f-g$	$f^{'}-g^{'}$
product	$fg$	$fg^{'}+f^{'}g$
quotient	$f/g$	$(fg^{'}+f^{'}g)/g^{2}$
chain(using $\frac{d}{dx}$ )		$\frac{dy}{dx}=\frac{dy}{du}\frac{du}{dx}$

Chain rule

$\frac{\partial y}{\partial x}=\frac{\partial y}{\partial u}\frac{\partial u}{\partial x}$
$y_{1}=xw_{1}+b_{1}$
$y_{2}=y_{1}w_{2}+b_{2}$
$y_{1}$ 为中间变量
$\frac{\partial y_{2}}{\partial w_{1}}=\frac{\partial f(y_{1})}{\partial w_{1}}=\frac{\partial f(y_{1})}{\partial y_{1}}\frac{\partial y_{1}}{\partial w_{1}}=w_{2}*x$
深度学习与PyTorch笔记14
从复杂到简单。

深度学习与PyTorch笔记14

链式法则

Derivative Rules

Chain rule

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