If \(y = \frac{1+x}{1-x}\), find \(\frac{dy}{dx}\).
FURTHER MATHEMATICS
WAEC 2017
If \(y = \frac{1+x}{1-x}\), find \(\frac{dy}{dx}\).
- A. \(\frac{2}{(1-x)^{2}}\)
- B. \(\frac{-2}{(1-x)^{2}}\)
- C. \(\frac{-1}{\sqrt{1-x}}\)
- D. \(\frac{1}{\sqrt{1-x}}\)
Correct Answer: A. \(\frac{2}{(1-x)^{2}}\)
Explanation
\(y = \frac{1+x}{1-x}\)
Using quotient rule, \(\frac{v\frac{du}{dx} - u\frac{dv}{dx}}{v^{2}}\), we have
\(\frac{dy}{dx} = \frac{(1-x)(1) - (1+x)(-1)}{(1-x)^{2}} = \frac{(1 - x +1 +x)}{(1-x)^{2}}\)
= \(\frac{2}{(1-x)^{2}}\).
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