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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

x = 0, y = x^{2}, y = x + 2

x \to - 1 lim (- 6)

9 x - (sin^{2} (2 x))

\frac{\partial}{\partial x} (x sin (y))

x^{2}, 8 - x^{2}, 4 x + 12

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