Can be written
(d/dx)(tan(x))=sec²(x)
Not sure what you’re asking for but tan(x)=sin(x)/cos(x).
If u=sin(x) and v=cos(x), tan(x)=u/v.
du/dx=cos(x), dv/dx=-sin(x),
(d/dx)(u/v)=[v(du/dx)-u(dv/dx)]/v²,
(d/dx)(tan(x))=[cos²(x)-(-sin²(x))]/cos²(x)=
[cos²(x)+sin²(x)]/cos²(x)=1/cos²(x).