en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of x^2arctan(6x)

Solution

\frac{d}{d x} (x^{2} arctan (6 x))

Solution

2 x arctan (6 x) + \frac{6 x ^{2}}{36 x ^{2} + 1}

Solution steps

\frac{d}{d x} (x^{2} arctan (6 x))

Apply the Product Rule:

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

f = x^{2}, g = arctan (6 x)

= \frac{d}{d x} (x^{2}) arctan (6 x) + \frac{d}{d x} (arctan (6 x)) x^{2}

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

\frac{d}{d x} (arctan (6 x)) = \frac{6}{36 x ^{2} + 1}

= 2 x arctan (6 x) + \frac{6}{36 x ^{2} + 1} x^{2}

Multiply fractions:

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

= 2 x arctan (6 x) + \frac{6 x ^{2}}{36 x ^{2} + 1}

Popular Examples

integral of (24x^2)/(sqrt(100-x^2))

\int \frac{24 x ^{2}}{100 - x ^{2}} d x

(dy)/(dx)=112yx^{15}

\frac{d y}{d x} = 112 y x^{15}

derivative of (x^2/(25))

\frac{d}{d x} (\frac{x ^{2}}{25})

derivative of ln(x/(sqrt(x^2+1)))

\frac{d}{d x} (ln (\frac{x}{x ^{2} + 1}))

(\partial)/(\partial x)(msin(2(mx+ny)))

\frac{\partial}{\partial x} (m sin (2 (m x + n y)))

Frequently Asked Questions (FAQ)

What is the derivative of x^2arctan(6x) ?
The derivative of x^2arctan(6x) is 2xarctan(6x)+(6x^2)/(36x^2+1)
What is the first derivative of x^2arctan(6x) ?
The first derivative of x^2arctan(6x) is 2xarctan(6x)+(6x^2)/(36x^2+1)