Derivative of $\frac{1}{x}$

The calculator will find the derivative of

\frac{1}{x}

, with steps shown.

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Your Input

Find $\frac{d}{dx} \left(\frac{1}{x}\right)$ .

Solution

Apply the power rule $\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$ with $n = -1$ :

{\color{red}\left(\frac{d}{dx} \left(\frac{1}{x}\right)\right)} = {\color{red}\left(- \frac{1}{x^{2}}\right)}

Thus, $\frac{d}{dx} \left(\frac{1}{x}\right) = - \frac{1}{x^{2}}$ .

Answer

$\frac{d}{dx} \left(\frac{1}{x}\right) = - \frac{1}{x^{2}}$ A