Find the derivative of f(x). f(x) = arctan(x) f′(x) = ______

Derivative rule for arctan function: To find the derivative of f(x) = arctan(x), we need to apply the derivative rule for the arctan function. The derivative of arctan(x) with respect to x is given by the formula: d/dx(arctan(x)) = 1/(1+x^2).Applying the derivative rule to f(x) = arctan(x): We apply the formula to f(x) = arctan(x) to find f′(x). f′(x) = 1/(1+x^2). This is the derivative of the arctan function, and there are no further simplifications needed.

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Find the derivative of $f(x)$ . $\newline$ $f(x) = \tan^{-1}{x}$ $\newline$ $f'(x) =$ ______

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Q. Find the derivative of

f(x)

\newline

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

\newline

f'(x) =

______

Derivative rule for arctan function: To find the derivative of $f(x) = \arctan(x)$ , we need to apply the derivative rule for the arctan function. $\newline$ The derivative of $\arctan(x)$ with respect to $x$ is given by the formula: $\frac{d}{dx}(\arctan(x)) = \frac{1}{1+x^2}$ .
Applying the derivative rule to $f(x) = \arctan(x)$ : We apply the formula to $f(x) = \arctan(x)$ to find $f'(x)$ . $\newline$ $f'(x) = \frac{1}{1+x^2}$ . $\newline$ This is the derivative of the $\arctan$ function, and there are no further simplifications needed.