en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of ln((e^t)/(1+e^t))

Solution

derivative of

ln (\frac{e ^{t}}{1 + e ^{t}})

Solution

1 - \frac{e ^{t}}{1 + e ^{t}}

Solution steps

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

Simplify

ln (\frac{e ^{t}}{1 + e ^{t}}) : t - ln (1 + e^{t})

= \frac{d}{d t} (t - ln (1 + e^{t}))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d t}{d t} - \frac{d}{d t} (ln (1 + e^{t}))

\frac{d t}{d t} = 1

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

= 1 - \frac{e ^{t}}{1 + e ^{t}}

Graph

Popular Examples

derivative of (8x^2-7y^3^5)

\frac{d}{d x} ((8 x^{2} - 7 y^{3})^{5})

integral of (4x^2+4x-6)/((x-6)(x-3)^2)

\int \frac{4 x ^{2} + 4 x - 6}{( x - 6 ) ( x - 3 ) ^{2}} d x

derivative of f(x)= 2/(x+1)derivative of

f (x) = \frac{2}{x + 1}

integral of (2x+4)/(x^2(x-2))

\int \frac{2 x + 4}{x ^{2} ( x - 2 )} d x

limit as x approaches-2 of x/(2x^2+2x+1)

x \to - 2 lim (\frac{x}{2 x ^{2} + 2 x + 1})

Frequently Asked Questions (FAQ)

What is the derivative of ln((e^t)/(1+e^t)) ?
The derivative of ln((e^t)/(1+e^t)) is 1-(e^t)/(1+e^t)
What is the first derivative of ln((e^t)/(1+e^t)) ?
The first derivative of ln((e^t)/(1+e^t)) is 1-(e^t)/(1+e^t)