Hey there i have defined this function: G[x_] := Log[x] and the nth derivative fnm[x_, n_] := Derivative[n][g][x]. When i try to print fnm[x, n], i just get the general answer g^(n)[x]. I am undable to get the answer as an explicit function in x. The furmulas are correct as i am able to get correct numeric results from them. What shall i do ?
Regards Andreas Ø (new user)
Derivative returns derivative function, which you then pass it the variable. So I would do it like this (I am assuming you are trying to define fnm to use for different functions.
G0 = Log;
fnm[fun_, n_] := Derivative[n][fun]
And now to use it
fnm[G0, 2][x]
(*-1/x^2*)
fnm[G0, n][x]
Derivative[n][Log][x]
%/.n->3
(*2/x^3*)
fnm[Sin, 3][x] (*etc....*)
If you just write fnm[G0, 2] you’ll get -(1/#1^2) &
Thanks for the answer, but unfortunately it will not give the explicit answer for the general case of n - it returns
Log^(n)(x) in stead of the actual expression in just n and x..
In case of n=2, it works fine, but that was not my problem..
but unfortunately it will not give the explicit answer for the general
case of n - it returns Log^(n)(x) in stead of the actual expression in
just n and x..
Ok, found a way. Use Lichtblau’s method as shown here.
nthDeriv[f_, x_, n_] := n!*SeriesCoefficient[f[x], {x, x, n}]
And now type
nthDeriv[Log, x, n]
gives
That worked! Thank you very much 
