Question

The length of sub-tangent to the curve $y=e^{\frac{x}{5}}$ is

Answer 1

Here, $y=e^{\frac{x}{5}}\cdots \left(i\right)$

$\Rightarrow \frac{dy}{dx}=e^{\frac{x}{5}}\frac{1}{5}\cdots \left(ii\right)$

And we know that the length of the sub-tangent $=\left|y\frac{dx}{dy}\right|$

$=|e^{\frac{x}{5}}\cdot \frac{5}{e^{\frac{x}{5}}}|=5$ [using $\left(i\right)$ and $\left(ii\right)$]