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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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