en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

derivative of [arctan(x](1+x^2))

Solution

\frac{d}{d x} ([arctan (x)] (1 + x^{2}))

Solution

1 + 2 x arctan (x)

Solution steps

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

Apply the Product Rule:

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

f = arctan (x), g = 1 + x^{2}

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

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

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

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

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

= 1 + 2 x arctan (x)

Graph

Popular Examples

integral of (x^2)/((1-16x^2)^{3/2)}

\int \frac{x ^{2}}{( 1 - 16 x ^{2} ) ^{\frac{3}{2}}} d x

integral of (x^5+7)/(x^2)

\int \frac{x ^{5} + 7}{x ^{2}} d x

derivative of 1/(sqrt(4+x^2))

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

derivative of sin(x+3cos(x))

\frac{d}{d x} (sin (x) + 3 cos (x))

integral of x^3sqrt(5-x^2)

\int x^{3} 5 - x^{2} d x

Frequently Asked Questions (FAQ)

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