Write the angle between the curves

Given that $y=e^{-x} \ldots(1)$ and $y=e^{x}$. .......(2)

Substituting the value of $y$ in (1),

$e^{-x}=e^{x}$

$\Rightarrow x=0$

And $y=1($ from 2$)$

On differentiating (1) w.r.t. $x$, we get

$\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{e}^{-x}$

$\Rightarrow \mathrm{m}_{2}=\frac{\mathrm{dy}}{\mathrm{dx}}=1$

$\because m_{1} \times m_{2}=-1$

Since the multiplication of both the slopes is $-1$ so the slopes are perpendicular to each other.

$\therefore$ Required angle $=90^{\circ}$