Calculus • Step-by-Step

Derivative of 1/x with Steps

Find the derivative of 1/x step by step. Rewrite the reciprocal as x^(-1) and apply the power rule d/dx[x^n] = n·x^(n-1) to find -1/x².

Problem Statement

\frac{d}{dx}[\frac{1}{x}]

Final Result

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

Formula Required: Negative Power Rule

Rewrite reciprocal terms with negative exponents before applying the power rule.

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

2 Steps

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

\frac{d}{dx} \left[ \frac{1}{x} \right]

Apply the Power Rule to compute the derivative.

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

Interactive Calculator

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

The graph of y = 1/x is strictly decreasing on both branches (for x < 0 and x > 0), so its slope is always negative: -1/x².