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

The derivative of x^2arctan(2x) is 2xarctan(2x)+(2x^2)/(4x^2+1)

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

The first derivative of x^2arctan(2x) is 2xarctan(2x)+(2x^2)/(4x^2+1)

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

2 x arctan (2 x) + \frac{2 x ^{2}}{4 x ^{2} + 1}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = arctan (2 x)

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

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

\frac{d}{d x} (arctan (2 x)) = \frac{2}{4 x ^{2} + 1}

= 2 x arctan (2 x) + \frac{2}{4 x ^{2} + 1} x^{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= 2 x arctan (2 x) + \frac{2 x ^{2}}{4 x ^{2} + 1}

\frac{d}{d x} (4 sin (x) - 4 x cos (x))

n = 3 \sum \infty \frac{1}{n ^{2} + 3 n}

\frac{\partial}{\partial x} (5 x + y)

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

f (x) = e^{x^{2} - 6}

What is the derivative of x^2arctan(2x) ?
The derivative of x^2arctan(2x) is 2xarctan(2x)+(2x^2)/(4x^2+1)
What is the first derivative of x^2arctan(2x) ?
The first derivative of x^2arctan(2x) is 2xarctan(2x)+(2x^2)/(4x^2+1)