Solution
= Solution
The requested base point is the <identity matrix> $I$, not the zero <matrix>. Since $I$ commutes with every $H$,
$$
\exp(I+H)=\exp(I)\exp(H)=e[I+H+O(\|H\|^2)].
$$
The <matrix> <power series> justifies the quadratic remainder near zero. Consequently
$$
\boxed{D\exp_I(H)=eH.}
$$
At zero the <derivative> would instead be $H$; replacing the printed base point would lose the scalar factor.