Q. If $y = \frac{e^{x} + e^{- x}}{e^{x} - e^{- x}},\ then\frac{dy}{dx}\ is\ equal\ to\$
A) ${sech}^{2}x$
B) ${cosech}^{2}\ x$
C) $- {sech}^{2}x$
D) $- {cosech}^{2}\ x$
Explanation
(d)
$y = \frac{\frac{(e^{x} + e^{- x})}{2}}{\frac{(e^{x} - e^{- x})}{2}}\ = \ \frac{\cosh x}{\sinh x}$
$\Rightarrow y\$= $\coth{x\ \Rightarrow \frac{dy}{dx} = - cosech^{2}\ x\ }$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.