CalcRef

Derivatives · Exponential & Logarithmic

Derivative of ln(x)

ddx[ln⁡x]=1x\frac{d}{dx}[\ln x] = \frac{1}{x}

The derivative of the natural logarithm is 1/x.

Conditions. x > 0.

Worked examples

Find d/dx[ln(x²)].
  1. Chain rule: (1/x²) · 2x = 2/x. Or simplify first: ln(x²) = 2 ln x, so d/dx = 2/x.

Answer: 2/x

Find d/dx[x ln x].
  1. Product rule: (1)(ln x) + (x)(1/x) = ln x + 1

Answer: ln x + 1

Related formulas

Derivative of log_a(x)

Practice this and 135 more formulas in the CalcRef workspace — quizzes, reference tables, a 16-category unit converter, and an expression evaluator.