What is the Derivative of Square Root x?

Derivative of Square Root x

The derivative of

\sqrt{x}

\frac{1}{2\sqrt{x}}

.

Solution. Let

f(x) = \sqrt{x}

. Then we can rewrite that as:

\begin{align*} f(x) = \sqrt{x} = x^{1/2}. \end{align*}

A simple fact from here says that

\frac{d}{dx} x^n = nx^{n-1}

. So we get:

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

Therefore, the derivative of

\sqrt{x}

\frac{1}{2\sqrt{x}}