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: Option A
Explanation
(y = frac{1+x}{1-x})
Using quotient rule, (frac{vfrac{du}{dx} – ufrac{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}}).