What is the derivative of f(x)=(e^x)/(1-e^x) ?

The derivative of f(x)=(e^x)/(1-e^x) is (e^x)/((1-e^x)^2)

What is the first derivative of f(x)=(e^x)/(1-e^x) ?

The first derivative of f(x)=(e^x)/(1-e^x) is (e^x)/((1-e^x)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

f (x) = \frac{e ^{x}}{1 - e ^{x}}

\frac{e ^{x}}{( 1 - e ^{x} ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

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

15 y^{^{''}} - 7 y^{^{'}} - 4 y = 0

t \to 0 lim (tan (4 t))

\int 2 t - 3 sin (t) d t

\frac{d}{d x} (6 x^{2} - 7 x)

\frac{d y}{d x} = \frac{3 y}{x}

What is the derivative of f(x)=(e^x)/(1-e^x) ?
The derivative of f(x)=(e^x)/(1-e^x) is (e^x)/((1-e^x)^2)
What is the first derivative of f(x)=(e^x)/(1-e^x) ?
The first derivative of f(x)=(e^x)/(1-e^x) is (e^x)/((1-e^x)^2)