What is the derivative of tan inverse of x

June 19, 2026Mathematics

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Answer

\frac{1}{1+x^2}

Step-by-step solution

2 steps

To find the derivative of the inverse tangent of $x$ , we use a standard differentiation formula.

Identify the function.
The function is $y = \arctan(x)$ .
Apply the derivative formula.
The derivative of $\arctan(x)$ with respect to $x$ is given by:
$\frac{d}{dx} (\arctan(x)) = \frac{1}{1+x^2}$
The derivative of $\tan^{-1}(x)$ is $\boxed{\frac{1}{1+x^2}}$ .

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