What is the derivative of e^xarctan(x) ?

The derivative of e^xarctan(x) is e^xarctan(x)+(e^x)/(x^2+1)

What is the first derivative of e^xarctan(x) ?

The first derivative of e^xarctan(x) is e^xarctan(x)+(e^x)/(x^2+1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply the Product Rule:

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

f = e^{x}, g = arctan (x)

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

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

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

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

\frac{1}{x ^{2} + 1} e^{x} = \frac{e ^{x}}{x ^{2} + 1}

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

x (\frac{d y}{d x}) = \frac{1}{y ^{3}}

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

\frac{e ^{x}}{5 + 5 x}

\frac{\partial}{\partial y} (e^{2 y} - y cos (x) y)

n = 1 \sum \infty (sin (8))^{n}

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