"Find the derivative of f(x)=tan−1(x)." solved and explained

Joan Thompson

Answered question

2021-12-13

Find the derivative of

f (x) = \tan^{- 1} (x)

alexandrebaud43

Beginner2021-12-14Added 36 answers

y = \arctan (x)

\tan (y) = x

\sec^{2} y \frac{d y}{d x} = 1

\frac{d y}{d x} = \frac{1}{\sec^{2} y}

Since

\tan (y) = \frac{x}{1}

and

\sqrt{1^{2} + x^{2}} = \sqrt{1 + x^{2}}

\sec^{2} y = {(\frac{\sqrt{1 + x^{2}}}{1})}^{2} = 1 + x^{2}

\Rightarrow \frac{d y}{d x} = \frac{1}{1 + x^{2}}

ambarakaq8

Beginner2021-12-15Added 31 answers

Apply the common derivative:

\frac{d}{d x} (\arctan (x)) = \frac{1}{x^{2} + 1}

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