Differentiation Question 218
Question: If $ y=\frac{\sqrt{x^{2}+1}+\sqrt{x^{2}-1}}{\sqrt{x^{2}+1}-\sqrt{x^{2}-1}} $ , then $ \frac{dy}{dx}= $
Options:
A) $ 2x+\frac{2x^{3}}{\sqrt{x^{4}-1}} $
B) $ 2x+\frac{x^{3}}{\sqrt{x^{4}-1}} $
C) $ x+\frac{2x^{3}}{\sqrt{x^{4}-1}} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Rationalising, $ y=\frac{2x^{2}+2\sqrt{x^{4}-1}}{2}=x^{2}+{{(x^{4}-1)}^{1/2}} $
Therefore $ \frac{dy}{dx}=2x+\frac{2x^{3}}{\sqrt{x^{4}-1}} $ .
BETA
