What is the derivative of ln(1+e^{x+1}) ?

The derivative of ln(1+e^{x+1}) is (e^{x+1})/(1+e^{x+1)}

What is the first derivative of ln(1+e^{x+1}) ?

The first derivative of ln(1+e^{x+1}) is (e^{x+1})/(1+e^{x+1)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

ln (1 + e^{x + 1})

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (\frac{1}{x ^{20}})

\frac{d}{d x} (- \frac{12}{x ^{3}})

\int \frac{1}{2} t cos (4) t^{2} d t

\frac{d}{d y} (y + 1)

\int 6 x + 5 d x

What is the derivative of ln(1+e^{x+1}) ?
The derivative of ln(1+e^{x+1}) is (e^{x+1})/(1+e^{x+1)}
What is the first derivative of ln(1+e^{x+1}) ?
The first derivative of ln(1+e^{x+1}) is (e^{x+1})/(1+e^{x+1)}