What is the derivative of xarctan(2x) ?

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

What is the first derivative of xarctan(2x) ?

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

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Popular >

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

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = arctan (2 x)

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

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

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

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

Simplify

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

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

x \to 0 - lim (x csc (x))

\frac{d ^{2}}{d x ^{2}} (cos (- 2 x))

\frac{d}{d x} (cos (x^{2} + π))

g (t) = 2^{t}

x^{2} e^{x - 1}, at 1

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