What is the derivative of (arctan(x)/x) ?

The derivative of (arctan(x)/x) is (x-arctan(x)(x^2+1))/(x^2(x^2+1))

What is the first derivative of (arctan(x)/x) ?

The first derivative of (arctan(x)/x) is (x-arctan(x)(x^2+1))/(x^2(x^2+1))

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\frac{d}{d x} (\frac{arctan ( x )}{x})

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

Solution steps

\frac{d}{d x} (\frac{arctan ( x )}{x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d x}{d x} = 1

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

Simplify

\frac{\frac{1}{x ^{2} + 1} x - 1 \cdot arctan ( x )}{x ^{2}} : \frac{x - arctan ( x ) ( x ^{2} + 1 )}{x ^{2} ( x ^{2} + 1 )}

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

What is the derivative of (arctan(x)/x) ?
The derivative of (arctan(x)/x) is (x-arctan(x)(x^2+1))/(x^2(x^2+1))
What is the first derivative of (arctan(x)/x) ?
The first derivative of (arctan(x)/x) is (x-arctan(x)(x^2+1))/(x^2(x^2+1))