Calculus • Step-by-Step

Derivative of ln(x) with Steps

Find the derivative of the natural logarithm ln(x) step by step. Shows formula and derivation d/dx[ln(x)] = 1/x for x > 0.

Problem Statement

\frac{d}{dx}[\ln(x)]

Final Result

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

Formula Required: Natural Logarithm Derivative

The rate of change of the natural log function is inversely proportional to x.

\frac{d}{dx}[\ln(x)] = \frac{1}{x} \quad (x > 0)

2 Steps

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

\frac{d}{dx} \left[ \mathrm{log}\left(x\right) \right]

Apply the Natural Log Rule to compute the derivative.

\frac{d}{dx} \left[ \mathrm{log}\left(x\right) \right] = \frac{1}{x}

Interactive Calculator

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

Since ln(x) is only defined for x > 0, its derivative 1/x is also restricted to x > 0 in this context.