Differentiation Question 439
Question: $ \frac{d}{dx}[ \log { e^{x}{{( \frac{x+2}{x-2} )}^{3/4}} } ] $ equals
Options:
A) $ \frac{x^{2}-7}{x^{2}-4} $
B) 1
C) $ \frac{x^{2}+1}{x^{2}-4} $
D) $ e^{x}\frac{x^{2}-1}{x^{2}-4} $
Show Answer
Answer:
Correct Answer: A
Solution:
$ y=\log e^{x}+\frac{3}{4}\log \frac{x+2}{x-2}=x+\frac{3}{4}\log \frac{x+2}{x-2} $
Therefore $ y=x+\frac{3}{4}[ \log (x+2)-\log (x-2) ] $
$ \frac{dy}{dx}=1+\frac{3}{4}[ \frac{1}{x+2}-\frac{1}{x-2} ]=1-\frac{3}{x^{2}-4} $
$ \frac{dy}{dx}=\frac{x^{2}-7}{x^{2}-4} $ .
BETA
