The subtangent of the curve $\mathrm{y}={\mathrm{e}}^{\frac{\mathrm{x}}{\mathrm{m}}}$ at $\mathrm{x}=\mathrm{m}$ is

The given curve is $\mathrm{y}={\mathrm{e}}^{\frac{\mathrm{x}}{\mathrm{m}}}$ and 

The given point is at $x=m$

Substitute $x=m$ in the equation, then $y=e$

Hence the given point is $\left(m,e\right)$

$\frac{dy}{dx}=\frac{1}{m}\left(e^{\frac{x}{m}}\right)$ at the point $\left(m,e\right)$ is $\frac{dy}{dx}=\frac{1}{m}e$

The length of the subtangent to the curve at the point$\left(x_1,y_1\right)$ is $\frac{y_1}{slope}$

Hence, length of the subtangent is $\frac{e}{{\displaystyle \raisebox{1ex}{$e$}\!\left/ \!\raisebox{-1ex}{$m$}\right.}}=\boxed{m}$