Differentiation Question 305
Question: $ \frac{d}{dx}[ \log { e^{x}{{( \frac{x-2}{x+2} )}^{3/4}} } ] $ equals to
[RPET 2001]
Options:
A) 1
B) $ \frac{x^{2}+1}{x^{2}-4} $
C) $ \frac{x^{2}-1}{x^{2}-4} $
D) $ e^{x}\frac{x^{2}-1}{x^{2}-4} $
Show Answer
Answer:
Correct Answer: C
Solution:
Let $ y=[ \log { e^{x}{{( \frac{x-2}{x+2} )}^{3/4}} } ]=\log e^{x}+\log {{( \frac{x-2}{x+2} )}^{3/4}} $
Therefore $ y=x+\frac{3}{4}[\log (x-2)-\log (x+2)] $
Therefore $ \frac{dy}{dx}=1+\frac{3}{4}[ \frac{1}{x-2}-\frac{1}{x+2} ]=1+\frac{3}{(x^{2}-4)} $
Therefore $ \frac{dy}{dx}=\frac{x^{2}-1}{x^{2}-4} $ .
BETA
