CalcRef

Derivatives · Inverse Trigonometric

Derivative of arctan(x)

ddx[arctan⁡x]=11+x2\frac{d}{dx}[\arctan x] = \frac{1}{1 + x^2}

The derivative of the inverse tangent function. Valid for all real x.

  • 2 worked examples
  • 24 in Derivatives

Worked examples

Find d/dx[arctan(3x)].
  1. Chain rule: 1/(1+(3x)²) · 3 = 3/(1+9x²)

Answer: 3/(1 + 9x²)

1 more worked examplePremium

Find d/dx[x arctan x].

Step-by-step solution locked.

Unlock the full working. CalcRef Premium opens the step-by-step solution above, and 141 worked solutions across the whole library - the intermediate lines, not just the answer. The formula statement, its conditions, its variables and the first worked example stay free on every page.
See PremiumBrowse the free reference

Related formulas

Derivative of arcsin(x)Derivative of arccos(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 arctan(x)?

The derivative of the inverse tangent function. Valid for all real x. It is one of the derivatives formulas in the CalcRef reference.

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

Worked example. Find d/dx[arctan(3x)]. Chain rule: 1/(1+(3x)²) · 3 = 3/(1+9x²). Answer: 3/(1 + 9x²).

Practice

Quiz yourself on Derivatives

Derivative of arctan(x) is one of 24 Derivatives formulas in CalcRef, out of 136 in the library. Today's free round is 10 mixed multiple-choice questions drawn from the same dataset as this page, refreshed every day and replayable as often as you like - no account needed.

Take today's free quizAll 24 Derivatives formulas