What is the derivative of-1/x ?

The derivative of-1/x is 1/(x^2)

What is the first derivative of-1/x ?

The first derivative of-1/x is 1/(x^2)

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derivative

\frac{1}{x ^{2}}

Solution steps

\frac{d}{d x} (- \frac{1}{x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{d}{d x} (\frac{1}{x})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= - \frac{d}{d x} (x^{- 1})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= - (- 1 \cdot x^{- 1 - 1})

Simplify

- (- 1 \cdot x^{- 1 - 1}) : \frac{1}{x ^{2}}

= \frac{1}{x ^{2}}