If x = \,y+1/y-1 then \,d y/d x is

Correct Answer is : −2(x−1)2\,-2/(x-1)²(x−1)2−2

Correct Answer is : −2(x−1)2\,-2/(x-1)²(x−1)2−2

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Differential Calculus

Question : 16 of 69

Marks: +1, -0

x = \,\frac{y+1}{y-1}

\,\frac{d y}{d x}

Solution:

Concept:

Express

y

in terms of

x

and differentiate.

Explanation:

Given

x = \frac{y+1}{y-1}

Cross-multiply:

x(y-1) = y+1

\Rightarrow xy - x = y + 1

\Rightarrow xy - y = x + 1

\Rightarrow y(x-1) = x+1

\Rightarrow y = \frac{x+1}{x-1}

Differentiate with respect to

x

using quotient rule:

\frac{dy}{dx} = \frac{(x-1)(1) - (x+1)(1)}{(x-1)^2}

\Rightarrow \frac{dy}{dx} = \frac{x-1 - x -1}{(x-1)^2} = \frac{-2}{(x-1)^2}

Answer:

\frac{dy}{dx} = \frac{-2}{(x-1)^2}

, which corresponds to option B.

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