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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 $\mathbf{Sy}$?2012-02-10
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    Seems to be a matrix-vector product...2012-02-10
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    Your lecture / text / notes *should* have a multivariable form of the chain rule, like $$\frac{d f}{d t}=\sum_{i=1}^n \frac{\partial f}{\partial x_i}\frac{\partial x_i}{\partial t}.$$2012-02-10
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    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: http://en.wikipedia.org/wiki/Partial_derivative and also http://en.wikipedia.org/wiki/Gradient. That has all you need (I presume you are really asking about what is explained in the second link).2012-02-10

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