OK, I suppose Mathematica isn't going to answer my real question. Which is: Let u(x) be any infinitely differentiable function. Then if f(x) = exp(u(x)), its nth derivative f^(n)(x) (n >= 1) is a polynomial with positive integer coefficients in the derivatives u', u'', ..., u^(n), times exp(u(x)): f^(n)(x) = P_n(u', u'', ..., u^(n)) exp(u(x)) The polynomial P will be homogenous of (let's call it) "index" n if in each monomial, the factor u^(k) is assigned index k, and the indices of all factors are added. Using x_1,...,x_n as the variables in P_n, we'd have for instance P_3(x_1, x_2, x_3) = (x_1)^3 + 3 x_1 x_2 + x_3 Question: Is there a closed formula for P_n (without recursion) ? Do they have a specific name? What properties do they have? --Dan