# Matrix Calculus example

How do I use chain rule to calculate the derivative of $h(\textbf{x})$, where $h(\textbf{x}) = f(\textbf{Sx}), f:R^n \to R$ and $\textbf{S}$ is a matrix.

I know how to use chain rule to compute derivative of single variable functions, and I know basic operations on matrix and vectors. But I'm not sure how to use chain rule on matrix functions. Any reference will be appreciated.

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What is $\mathbf{Sy}$? –  William Feb 10 '12 at 6:29
Seems to be a matrix-vector product... –  Ｊ. Ｍ. Feb 10 '12 at 6:40
Your lecture / text / notes should have a multivariable form of the chain rule, like $$\frac{d f}{d t}=\sum_{i=1}^n \frac{\partial f}{\partial x_i}\frac{\partial x_i}{\partial t}.$$ –  anon Feb 10 '12 at 7:22
OK, so changing $\mathbf{y}$ to $\mathbf{x}$ didn't really clarify anything, but I'll go with J. M.'s assumption. Here you go: en.wikipedia.org/wiki/Partial_derivative and also en.wikipedia.org/wiki/Gradient. That has all you need (I presume you are really asking about what is explained in the second link). –  William Feb 10 '12 at 7:25