Q. The length of the subtangent at any point $(x_{1},\ y_{1})$on the curve $y = a^{x},\ (a > 0)$ is
A) $2\log a$
B) $\frac{1}{\log a}$
C) $\log a$
D) $a^{2x_{1}}\log a$
Explanation
(b)
Given, $y = a^{x}\ \ \ \ \Rightarrow \ \ \ \ \frac{dy}{dx} = a^{x}\log a$
Now, length of subtangent at any point $(x_{1},\ \ y_{1})$
$= \frac{y}{dy/dx} = \frac{a^{x_{1}}}{a^{x_{1}}\log a} = \frac{1}{\log a}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.