05/25/2009, 12:13 PM
(05/25/2009, 09:31 AM)Ansus Wrote: Great! I've added the rule to our wiki page http://en.wikipedia.org/wiki/User:MathFa...on_Summary
\( (\operatorname{sexp}_x(1))'=1 \)
\( (\operatorname{sexp}_x(n))'=\left((\operatorname{sexp}_x(n-1))'\ln x + \frac{\operatorname{sexp}_x(n-1)}{x}\right)\operatorname{sexp}_x(n) \)
This works also for arbitrary complex \( n=:y \):
\( \frac{\partial}{\partial x} x[4](y+1) = \frac{\partial}{\partial x} x^{x[4]y} =
\frac{\partial}{\partial x} \exp(\ln(x)(x[4]y)) = (x[4](y+1)) \cdot \left(\frac{x[4]y}{x} +\ln(x) \frac{\partial}{\partial x} x[4]y\right) \)
