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

The derivative of y=(arctan(2x))/x is (2x-arctan(2x)(4x^2+1))/(x^2(4x^2+1))

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

The first derivative of y=(arctan(2x))/x is (2x-arctan(2x)(4x^2+1))/(x^2(4x^2+1))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

y = \frac{arctan ( 2 x )}{x}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

x \to 0 lim ((x + 1)^{l n (x)})

f (x) = 9 + 5 x^{2} - 2 x^{3}

\frac{d}{d x} (x^{3} 3^{x})

\int_{1}^{4} ln (x) d x

\frac{d}{d x} (e^{2 x^{5}})

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