# Formulas for the multivariate Gaussian function?

I wonder if anyone has formulas for the derivatives of $f(x)=(2\pi)^{-n/2}|\Sigma|^{-1/2}\exp \{-\frac{1}{2}x^t \Sigma^{-1} x\}$ or for instance, for,

$$\int_{\mathbb{R}^n}D^{\alpha}f(x)dx$$

is there any website or book where I can find these?

Thanks you very much!

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If you convert the density function to use the actual elements of $x$ and $\Sigma$ rather than the matrix equivalents, taking derivatives will become more clear. –  Max Oct 26 '12 at 16:39
Will this involve Hermite polynomials? –  Michael Hardy Oct 26 '12 at 17:34