We know that, $f:\mathbb{R}\to \mathbb{R}$ satisfies ${f}^{\prime}(x)=f(x)$ for all $x\in \mathbb{R}$ then $f(x)=A{e}^{x}$

What is a function $f:{\mathbb{R}}^{d}\to {\mathbb{R}}^{d}$, analogous to the exponential function, if $\mathbf{x}\in {\mathbb{R}}^{d}$ was a d dimensional vector?

Is there a name given to such functions whose derivatives are the same as the function itself?

What is a function $f:{\mathbb{R}}^{d}\to {\mathbb{R}}^{d}$, analogous to the exponential function, if $\mathbf{x}\in {\mathbb{R}}^{d}$ was a d dimensional vector?

Is there a name given to such functions whose derivatives are the same as the function itself?