en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of sqrt(arctan(x))

Solution

derivative of

arctan (x)

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

Popular Examples

integral of 2/3 x(a^2+x^2)^{3/2}

\int \frac{2}{3} x (a^{2} + x^{2})^{\frac{3}{2}} d x

derivative of (sqrt(s)-1)/(sqrt(s)+7)derivative of

\frac{s - 1}{s + 7}

integral of ln(1+t)

\int ln (1 + t) d t

integral of e^{-x/(100)}

\int e^{- \frac{x}{100}} d x

integral of 15x^2e^{5x^3-6}

\int 15 x^{2} e^{5 x^{3} - 6} d x

Frequently Asked Questions (FAQ)

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