What is the derivative of y=arctan(e^x) ?

The derivative of y=arctan(e^x) is (e^x)/(e^{2x)+1}

What is the first derivative of y=arctan(e^x) ?

The first derivative of y=arctan(e^x) is (e^x)/(e^{2x)+1}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

y = arctan (e^{x})

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

What is the derivative of y=arctan(e^x) ?
The derivative of y=arctan(e^x) is (e^x)/(e^{2x)+1}
What is the first derivative of y=arctan(e^x) ?
The first derivative of y=arctan(e^x) is (e^x)/(e^{2x)+1}