Differentiation Question 271
Question: $ \frac{d}{dx}{ \log ( \frac{e^{x}}{1+e^{x}} ) }= $
Options:
A) $ \frac{1}{1-e^{x}} $
B) $ -\frac{1}{1+e^{x}} $
C) $ -\frac{1}{1-e^{x}} $
D) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
$ \frac{d}{dx}\log ( \frac{e^{x}}{1+e^{x}} )=\frac{1+e^{x}}{e^{x}}\times \frac{d}{dx}( \frac{e^{x}}{1+e^{x}} ) $
$ =\frac{1+e^{x}}{e^{x}}\times \frac{e^{x}}{{{(1+e^{x})}^{2}}}=\frac{1}{1+e^{x}} $ .
BETA
