What is the Derivative of 1/x?

Derivative of 1/x

The derivative of

\frac{1}{x}

\frac{-1}{x^2}

.

Solution. Let

f(x) = \frac{1}{x}

. Then this can be rewritten as

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

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:

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

So, the derivative of

\frac{1}{x}

\frac{-1}{x^2}