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What's the general expression of $\dfrac{d ^n e^{f(x)}}{d x^n}$ in term of derivative $\dfrac{d f(x)}{d x}$, $\dfrac{d ^2e^{f(x)}}{d x^2}$,$\dfrac{d ^3e^{f(x)}}{d x^3},\dots$?

Actually I wonder whether there is a special expression for the series of coefficients for different integers $n$? Some of the series: $(1),(1,1),(1,3,1),(1,6,4,3,1),(1,10,10,5,15,10,1)\dots$

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    This http://en.wikipedia.org/wiki/Fa%C3%A0_di_Bruno%27s_formula can help you.2012-07-18
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    Why are you using partial derivative notation? Is your function a function of several variables, or just one?2012-07-18
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    @Arturo Magidin sorry for my misleading expression;i've already edited my question. Here i only consider the one variable case.( the original expression is copied from Mathematica, so it is in term of partial derivative)2012-07-18

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