The function powdiff(p) returns the formal power series that is the derivative of p with respect to the variable of p.

The command with(powseries,powdiff) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{powseries}\right)\:$

$t≔\mathrm{powpoly}\left(x+1\,x\right)\:$

$s≔\mathrm{powlog}\left(t\right)\:$

$\mathrm{tpsform}\left(s\,x\,6\right)$

$x-\frac{1}{2}{x}^2+\frac{1}{3}{x}^3-\frac{1}{4}{x}^4+\frac{1}{5}{x}^5+O\left(x^6\right)$

$r≔\mathrm{powdiff}\left(s\right)\:$

$\mathrm{tpsform}\left(r\,x\,10\right)$

$1-x+x^2-x^3+x^4-x^5+x^6-x^7+x^8-x^9+O\left(x^{10}\right)$