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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

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

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

x \to + 4 lim (\frac{3 x}{4} + 2)

\frac{\partial}{\partial x} (2 e^{x^{8} y})

9 y^{^{''}} + 9 y^{^{'}} - 4 y = 0

x \to 0 lim (x cos (\frac{9}{x}))

\frac{d ^{2}}{d x ^{2}} (\frac{7}{8 t ^{5}})

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