Simon Hanna

2022-11-28

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

Callum Richmond

Expert

Identify the derivative of$\frac{1}{x}$.
Let$\frac{1}{x}={x}^{-1}.$
Next, determine the derivative of ${x}^{-1}$ that can be defined as follows:
$\frac{d}{dx}\left({x}^{-1}\right)=-1{x}^{-1-1}\left(\because \frac{d}{dx}\left({x}^{n}\right)=n{x}^{n-1}\right)⇒=-1{x}^{-2}⇒=-{x}^{-2}$
Hence, the derivative of $\frac{1}{x}$ is $"-{x}^{-2}"$.

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