What is the derivative of $\frac{1}{x}$ $1/x$ ?

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What is the derivative of $\frac{1}{x}$ $1/x$ ?

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Answer 1 · 2016-04-15T20:05:49

$- \frac{1}{x^{2}}$ $-1/x^2$

Explanation:

First step is to write $\frac{1}{x} as x^{- 1} and apply the power rule$ $1/x " as " x^-1 " and apply the power rule "$

$\Rightarrow \frac{d}{d x} (x^{- 1}) = - 1 x^{- 2} = - \frac{1}{x^{2}}$ $rArr d/dx(x^-1) = -1 x^-2 = -1/x^2$

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What is the derivative of $\frac{1}{x}$ $1/x$ ?

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