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^{7x}/(1+e^{7x)}))

Solution

\frac{d}{d x} (ln (\frac{e ^{7 x}}{1 + e ^{7 x}}))

Solution

7 - \frac{7 e ^{7 x}}{1 + e ^{7 x}}

Solution steps

\frac{d}{d x} (ln (\frac{e ^{7 x}}{1 + e ^{7 x}}))

Simplify

ln (\frac{e ^{7 x}}{1 + e ^{7 x}}) : 7 x - ln (1 + e^{7 x})

= \frac{d}{d x} (7 x - ln (1 + e^{7 x}))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (7 x) - \frac{d}{d x} (ln (1 + e^{7 x}))

\frac{d}{d x} (7 x) = 7

\frac{d}{d x} (ln (1 + e^{7 x})) = \frac{7 e ^{7 x}}{1 + e ^{7 x}}

= 7 - \frac{7 e ^{7 x}}{1 + e ^{7 x}}

Popular Examples

derivative of 3tan^2(2x)derivative of

3 tan^{2} (2 x)

integral from 1 to 2 of 3/(x^3+4x)

\int_{1}^{2} \frac{3}{x ^{3} + 4 x} d x

(\partial)/(\partial x)(x^{1/3})

\frac{\partial}{\partial x} (x^{\frac{1}{3}})

sum from n=1 to infinity}(-1)^{n+1 of n

n = 1 \sum \infty (- 1)^{n + 1} n

derivative of sqrt(\sqrt{x+1)+1}

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

Frequently Asked Questions (FAQ)

What is the derivative of ln((e^{7x}/(1+e^{7x)})) ?
The derivative of ln((e^{7x}/(1+e^{7x)})) is 7-(7e^{7x})/(1+e^{7x)}
What is the first derivative of ln((e^{7x}/(1+e^{7x)})) ?
The first derivative of ln((e^{7x}/(1+e^{7x)})) is 7-(7e^{7x})/(1+e^{7x)}