Differentiation Question 328
Question: If $ y=\frac{e^{x}+{e^{-x}}}{e^{x}-{e^{-x}}} $ then $ \frac{dy}{dx} $ is equal to
[Karnataka CET 2005]
Options:
A) $ \sec {h^{2}}x $
B) $ cosec{h^{2}}x $
C) $ -\sec {h^{2}}x $
D) $ -cosec{h^{2}}x $
Show Answer
Answer:
Correct Answer: D
Solution:
$ y=\frac{e^{x}+{e^{-x}}}{e^{x}-{e^{-x}}}=\frac{\frac{e^{x}+{e^{-x}}}{2}}{\frac{e^{x}-{e^{-x}}}{2}}=\frac{\cosh x}{\sinh x}=\coth x $
$ \frac{dy}{dx}=-cosec{h^{2}}x $ .
BETA
