Question

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

Answer 1

Determine the derivative of $\frac{1}{x}$.

Let$\frac{1}{x}=x^{-1}.$

Now calculate the derivative of $x^{-1}$ that can be defined as follows:

$$\begin{gathered} \frac{d}{dx}\left(x^{-1}\right)=-1x^{-1-1}\left[\because \frac{d}{dx}\left(x^n\right)=n{x}^{n-1}\right] \\ \Rightarrow =-1x^{-2} \\ \Rightarrow =-x^{-2} \end{gathered}$$

Hence, the derivative of $\frac{1}{x}$ is $"-x^{-2}"$.