A Chain Inside a Chain — hard The Multivariate Chain Rule problem | Incognition

A Chain Inside a Chain

30 pts · 30 coins

The Multivariate Chain RuleHard

A Chain Inside a Chain

A computational graph has three layers between the input $t$ and the output $g$ :

Node	Definition
$x$	$t + 1$
$y$	$t^2$
$u$	$x^2 + y^2$
$v$	$x - y$
$g$	$u / v$

Both $x$ and $y$ fan out into both $u$ and $v$ .

What is $\dfrac{dg}{dt}$ at $t = 1$ ?

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