What is the derivative of x^3arctan(3x) ?

The derivative of x^3arctan(3x) is 3x^2arctan(3x)+(3x^3)/(9x^2+1)

What is the first derivative of x^3arctan(3x) ?

The first derivative of x^3arctan(3x) is 3x^2arctan(3x)+(3x^3)/(9x^2+1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

3 x^{2} arctan (3 x) + \frac{3 x ^{3}}{9 x ^{2} + 1}

Solution steps

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

Apply the Product Rule:

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

f = x^{3}, g = arctan (3 x)

= \frac{d}{d x} (x^{3}) arctan (3 x) + \frac{d}{d x} (arctan (3 x)) x^{3}

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} (arctan (3 x)) = \frac{3}{9 x ^{2} + 1}

= 3 x^{2} arctan (3 x) + \frac{3}{9 x ^{2} + 1} x^{3}

Multiply fractions:

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

= 3 x^{2} arctan (3 x) + \frac{3 x ^{3}}{9 x ^{2} + 1}

What is the derivative of x^3arctan(3x) ?
The derivative of x^3arctan(3x) is 3x^2arctan(3x)+(3x^3)/(9x^2+1)
What is the first derivative of x^3arctan(3x) ?
The first derivative of x^3arctan(3x) is 3x^2arctan(3x)+(3x^3)/(9x^2+1)