Answer
The statement is true.
Work Step by Step
A transformation is said to be linear if $T(av+w)=aT(v)+T(w)$, for all $ v,w$ in the given domain and for all scalars $a$.
Here, $T=D_x$. Since $D_x$ is a linear transformation.
$D_x(e^{x^2}+2x)=D_x(e^{x^2})+2D_x(x)$
