Question 578370
the Maclaurin series of f(x) = e^x
{{{e^x=1+x+x^2/2!+x^3/3!+x^4/4!}}}+...
then d/dx {{{e^x}}} =d/dx ({{{1+x+x^2/2!+x^3/3!+x^4/4!}}}+...)={{{0+1+2x/2!+3x^2/3!+4x^3/3!}}}+...={{{1+x+x^2/2!+x^3/3!}}}+...={{{e^x}}}