What is the derivative of (x^2/(arctan(x))) ?

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

What is the first derivative of (x^2/(arctan(x))) ?

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

y = ln (sec (5 x) + tan (5 x))

\frac{d}{d x} (\frac{1}{x ^{5}} + e^{x})

\int \frac{1}{x ( 1 - x )} d x

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

\frac{d}{d x} ((3 x^{2} - x)^{7})

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