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.

Worked examples

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

Answer: 3/(1 + 9x²)

Find d/dx[x arctan x].
  1. Product rule: (1)(arctan x) + (x)(1/(1+x²))
  2. = arctan x + x/(1+x²)

Answer: arctan x + x/(1 + x²)

Related formulas

Derivative of arcsin(x)Derivative of arccos(x)

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