**Solution.**Let f(x) = \frac{1}{x}. Then this can be rewritten as

\begin{align*} f(x) = x^{-1}. \end{align*}

\begin{align*} f'(x) = (-1) \cdot x^{-1 - 1} = -x^{-2}. \end{align*}

Skip to content
## What is the Derivative of 1/x?

The derivative of \frac{1}{x} is \frac{-1}{x^2}.

**Solution.** Let f(x) = \frac{1}{x}. Then this can be rewritten as
Now it is relatively easy to determine the derivative, as we have seen here that \frac{d}{dx} x^n = nx^{n-1}. Since n = -1, we have that:
So, the derivative of \frac{1}{x} is \frac{-1}{x^2}.

\begin{align*} f(x) = x^{-1}. \end{align*}

\begin{align*} f'(x) = (-1) \cdot x^{-1 - 1} = -x^{-2}. \end{align*}