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DerivativesCalculusCollegeabout 0:43

Find d/dx arctan(x): animated lesson

A narrated, step-by-step derivatives video lesson with captions. Final answer: f'(x) = 1 / (x² + 1).

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Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.3 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Finding a derivative
$\frac{d}{dx}\left[\tan^{-1}\left( x\right)\right]$
2. Step by step
1. $\frac{d}{dx}\left[\tan^{-1}\left( x\right)\right] = \frac{1}{{x}^{2}+1}$
  d/dx[arctan x] = 1/(1 + x²)
2. $f'(x) = \frac{1}{{x}^{2}+1}$
  Combine and simplify
3. The answer
$f'(x) = \frac{1}{{x}^{2}+1}$
f'(x) = 1 / (x² + 1)
4. Check
- Cross-checked numerically against an independent symbolic differentiator at 8 sample points ✓

Transcript

The problem. Here is the problem: d by d x arctan(x). Find the derivative of atan(x) with respect to x.

Step by step. d by d x[arctan x] equals 1/(1 plus x squared). Combine and simplify.

The answer. So the answer is f prime of x equals 1 / (x squared plus 1). The derivative is built from the outside in: sums split into terms, constants factor out, products and quotients use their rules, and every composite function multiplies by the derivative of its inside (chain rule).

Check. Cross-checked numerically against an independent symbolic differentiator at 8 sample points, which checks out.

About derivatives

Differentiate with the power, product, quotient and chain rules, including higher derivatives.

Find d/dx arctan(x): Derivatives Step-by-Step Lesson