Calculus • Step-by-Step

Derivative of √x with Steps

Differentiate the square root of x step by step. Rewrite √x as x^(1/2) and apply the power rule to get 1/(2√x).

Problem Statement

\frac{d}{dx}[\sqrt{x}]

Final Result

f'(x) = \frac{1}{2 \cdot x^{\frac{1}{2}}}

Formula Required: Fractional Power Rule

Express root radicals as fractional powers before differentiating.

\frac{d}{dx}[x^{1/2}] = \frac{1}{2}x^{-1/2} = \frac{1}{2\sqrt{x}}

2 Steps

Set up the differentiation problem with respect to variable $x$.

\frac{d}{dx} \left[ \sqrt{x} \right]

Apply the Power Rule to compute the derivative.

\frac{d}{dx} \left[ \sqrt{x} \right] = \frac{1}{2 \cdot x^{\frac{1}{2}}}

Interactive Calculator

Enter any equation like 2x + 8 = 20 or x² - 5x + 6 = 0 to get step-by-step solutions.

Rewrite √x as x^(1/2). Bring down 1/2 and subtract 1: (1/2)x^(-1/2) = 1 / (2√x).