Let's assume I have a function $f(x)=\exp(10x^2)$, i.e.
f[x_]:= Exp[10*x^2]. When I differentiate $f$ by evaluating the expression
D[f[x],x], I get the result:
20 E^(10 x^2) x
which is OK, but I would like to see
20 f[x] x
Is there any way to force Mathematica to do this substitution?
I do not necessarily expect Mathematica to output this right away, but at least is there any command to replace expressions with predefined functions where possible?
This is just a simple example, but clearly you get the point. If then one works with much more complicated expressions, this can save a lot of space and supports nice analytical expressions.