I'm trying to find the n-order derivative of a function.
Function: $f(x) = x^3.lnx$
1.Derivative: $f'(x) = x^2.(3lnx+1)$
2.Derivative: $f''(x) = x.(6lnx+5)$
3.Derivative: $f'''(x) = (6lnx+11)$
4.Derivative: $f^{(4)}(x) = 6x^{-1}$
5.Derivative: $f^{(5)}(x) = -6x^{-2}$
6.Derivative: $f^{(6)}(x) = 12x^{-3}$
7.Derivative: $f^{(7)}(x) = -36x^{-4}$
8.Derivative: $f^{(8)}(x) = 144x^{-5}$
How can I write the general derivative of this function over n only thing I can find is for $x$
n.Derivative: $f^{(n)} = x^{n-3}..?$
Just guide me, I believe I will figure out the rest myself.