Differentiation Question 7
Question: If $ y=x^{2}+\frac{1}{x^{2}+\frac{1}{x^{2}+\frac{1}{x^{2}+……\infty }}}, $ then $ \frac{dy}{dx}= $
Options:
A) $ \frac{2xy}{2y-x^{2}} $
B) $ \frac{xy}{y+x^{2}} $
C) $ \frac{xy}{y-x^{2}} $
D) $ \frac{2xy}{2+\frac{x^{2}}{y}} $
Show Answer
Answer:
Correct Answer: A
Solution:
$ y=x^{2}+\frac{1}{y}\Rightarrow y^{2}=x^{2}y+1 $
$ \Rightarrow 2y\frac{dy}{dx}=y.2x+x^{2}\frac{dy}{dx} $
Therefore $ \frac{dy}{dx}=\frac{2xy}{2y-x^{2}} $ .
BETA
