# Multivariate derivatives cheatsheet

##### Calculus

We provide an easy to use reference for oft-used multivariate derivatives.

## Prerequisites

To understand and use these derivatives, we recommend familiarity with the concepts in

Follow the above links to first get acquainted with the corresponding concepts.

## Some oft-used derivatives

$\partial \mA$ 0
$\partial (\alpha \mX)$ $\alpha \partial \mX$
$\partial (\mX + \mY)$ $\partial \mX + \partial \mY$
$\partial (\mX\mY)$ $(\partial \mX)\mY + \mX(\partial \mY)$
$\partial \inv{\mX}$ $-\inv{\mX} \left( \partial \mX\right) \inv{\mX}$
$\partial \mX^T$ $\left(\partial \mX\right)^T$
$\partial \vx^T \va$ $\va$
$\partial \left(\va^T \mX \vb\right)$ $\va^T \vb$
$\partial \left(\va^T \mX^T \vb\right)$ $\vb \va^T$
$\partial \left(\norm{\vx - \va}{2}\right)$ $\frac{\vx - \va}{\norm{\vx - \va}{2}}$
$\partial \left(\norm{\mX}{2}\right)$ $2\mX$

## Where to next?

This was a quick reference for multivariate derivatives. Explore our other comprehensive articles on topics in calculus.

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