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Logarithmic Differentiation

The Exprssion...

Question

The Exprssion $(x + y)^{- 1} (x^{- 1} + y^{- 1})$ is equivalent to

1

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(x y)^{- 1}

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x^{y}

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x y^{- 1} + x^{- 1} y

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Solution

The correct option is B $(x y)^{- 1}$
$(x + y)^{- 1} (x^{- 1} + y^{- 1})$

$\Rightarrow \frac{1}{(x + y)} \times (\frac{1}{x} + \frac{1}{y})$

$\Rightarrow \frac{1}{(x + y)} \times (\frac{x + y}{x y})$

$\Rightarrow \frac{1}{x y}$

$\Rightarrow (x y)^{- 1}$

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