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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.
  • 2 worked examples
  • 24 in Derivatives

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

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Find d/dx[x ln x].

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Related formulas

Derivative of log_a(x)

See all 24 Derivatives formulas on one printable sheet - the same statements and conditions as these pages, typeset and laid out for paper.

Common questions

What is the Derivative of ln(x)?

The derivative of the natural logarithm is 1/x. It is one of the derivatives formulas in the CalcRef reference.

When does the Derivative of ln(x) apply?

The Derivative of ln(x) holds under this condition: x > 0.

How do you use the Derivative of ln(x)?

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

Practice

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