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Find the derivative of f(x) f(x) .\newlinef(x)=tan⁡−1x f(x) = \tan^{-1}{x} \newlinef′(x)= f'(x) = ______

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Q. Find the derivative of f(x) f(x) .\newlinef(x)=tan⁡−1x f(x) = \tan^{-1}{x} \newlinef′(x)= f'(x) = ______
  1. Derivative rule for arctan function: To find the derivative of f(x)=arctan⁡(x)f(x) = \arctan(x), we need to apply the derivative rule for the arctan function.\newlineThe derivative of arctan⁡(x)\arctan(x) with respect to xx is given by the formula: ddx(arctan⁡(x))=11+x2\frac{d}{dx}(\arctan(x)) = \frac{1}{1+x^2}.
  2. Applying the derivative rule to f(x)=arctan⁡(x)f(x) = \arctan(x): We apply the formula to f(x)=arctan⁡(x)f(x) = \arctan(x) to find f′(x)f'(x).\newlinef′(x)=11+x2f'(x) = \frac{1}{1+x^2}.\newlineThis is the derivative of the arctan⁡\arctan function, and there are no further simplifications needed.

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