What is the derivative of arctan(sqrt(x^2+2x)+C) ?

The derivative of arctan(sqrt(x^2+2x)+C) is 1/((x+1)sqrt(x^2+2x))

What is the first derivative of arctan(sqrt(x^2+2x)+C) ?

The first derivative of arctan(sqrt(x^2+2x)+C) is 1/((x+1)sqrt(x^2+2x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

Solution steps

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

Treat

C

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d C}{d x} = 0

= \frac{1}{( x + 1 ) x ^{2} + 2 x} + 0

Simplify

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

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