Write the angle between the curves


Write the angle between the curves $y=e^{-x}$ and $y=e^{x}$ at their point of intersection.


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

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


$\Rightarrow x=0$

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

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


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

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

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

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

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