What is the derivative of x^2arctan(9x) ?

The derivative of x^2arctan(9x) is 2xarctan(9x)+(9x^2)/(81x^2+1)

What is the first derivative of x^2arctan(9x) ?

The first derivative of x^2arctan(9x) is 2xarctan(9x)+(9x^2)/(81x^2+1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

x^{2} arctan (9 x)

2 x arctan (9 x) + \frac{9 x ^{2}}{81 x ^{2} + 1}

Solution steps

\frac{d}{d x} (x^{2} arctan (9 x))

Apply the Product Rule:

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

f = x^{2}, g = arctan (9 x)

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

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

\frac{d}{d x} (arctan (9 x)) = \frac{9}{81 x ^{2} + 1}

= 2 x arctan (9 x) + \frac{9}{81 x ^{2} + 1} x^{2}

Multiply fractions:

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

= 2 x arctan (9 x) + \frac{9 x ^{2}}{81 x ^{2} + 1}

y^{^{''}} - y = 2

x \to 15 lim (10)

y = x^{2} cos^{4} (x)

\int (tan (2 x)) d x

What is the derivative of x^2arctan(9x) ?
The derivative of x^2arctan(9x) is 2xarctan(9x)+(9x^2)/(81x^2+1)
What is the first derivative of x^2arctan(9x) ?
The first derivative of x^2arctan(9x) is 2xarctan(9x)+(9x^2)/(81x^2+1)