en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of y=ln(1+e^x)

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

(\partial)/(\partial x)(sin(5x-8y))

\frac{\partial}{\partial x} (sin (5 x - 8 y))

area e^x,e^{-3x},x=ln(3)area

e^{x}, e^{- 3 x}, x = ln (3)

integral of (9x+6)/((x-6)(x+4))

\int \frac{9 x + 6}{( x - 6 ) ( x + 4 )} d x

integral from 1 to 2 of (x+1)/(x(x^2+1))

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

derivative of y=ln(sqrt(x^2+4))derivative of

y = ln (x^{2} + 4)

Frequently Asked Questions (FAQ)

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