Backprop calculus

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Warm-up

   In a computational graph, $u = -2(x - 1)$ and $y = -2\,e^{u}$. Using the chain rule, find $\dfrac{dy}{dx}$ at $x = 1$.

2. Warm-up

   In a computational graph, $u = 2(x + 3)$ and $y = 4\,e^{u}$. Using the chain rule, find $\dfrac{dy}{dx}$ at $x = -3$.

3. Warm-up

   In a computational graph, $u = 2(x - 3)$ and $y = -4\,e^{u}$. Using the chain rule, find $\dfrac{dy}{dx}$ at $x = 3$.

Problems shown under their original terms: Generated (template, solver-computed).