How do you differentiate $y = \frac{a}{x - 1}$ $y = a / (x - 1)$ ?

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How do you differentiate $y = \frac{a}{x - 1}$ $y = a / (x - 1)$ ?

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Answer 1 · 2017-04-12T19:43:15

$\frac{d y}{d x} = - \frac{a}{{(x - 1)}^{2}}$ $dy/dx=-a/(x-1)^2$

Explanation:

$express y = \frac{a}{x - 1} = a {(x - 1)}^{- 1}$ $"express " y=a/(x-1)=a(x-1)^-1$

$\Rightarrow \frac{d y}{d x} = - a {(x - 1)}^{- 2} . \frac{d}{d x} (x - 1) \leftarrow chain rule$ $rArrdy/dx=-a(x-1)^-2.d/dx(x-1)larr" chain rule"$

$\Rightarrow \frac{d y}{d x} = - a {(x - 1)}^{- 2} = - \frac{a}{{(x - 1)}^{2}}$ $color(white)(rArrdy/dx)=-a(x-1)^-2=-a/(x-1)^2$

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How do you differentiate $y = \frac{a}{x - 1}$ $y = a / (x - 1)$ ?

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How do you differentiate y = a / (x - 1) y=ax−1y = a / (x - 1) ?

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How do you differentiate $y = \frac{a}{x - 1}$ $y = a / (x - 1)$ ?