What is the derivative of 1/(1+ln(x)) ?

The derivative of 1/(1+ln(x)) is -1/(x(1+ln(x))^2)

What is the first derivative of 1/(1+ln(x)) ?

The first derivative of 1/(1+ln(x)) is -1/(x(1+ln(x))^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

= - \frac{1}{( 1 + ln ( x ) ) ^{2}} \cdot \frac{1}{x}

Simplify

- \frac{1}{( 1 + ln ( x ) ) ^{2}} \cdot \frac{1}{x} : - \frac{1}{x ( 1 + ln ( x ) ) ^{2}}

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

y^{^{'}} - \frac{y}{x} = \frac{x y}{x}

\frac{d x}{d t} = x + \frac{t ^{2}}{2}, x (0) = 0

\frac{d}{d x} (\frac{1}{x ^{10}})

f (x) = \frac{5 x}{x - 3}, at (4)

\int \frac{2 + x + x}{x} d x

What is the derivative of 1/(1+ln(x)) ?
The derivative of 1/(1+ln(x)) is -1/(x(1+ln(x))^2)
What is the first derivative of 1/(1+ln(x)) ?
The first derivative of 1/(1+ln(x)) is -1/(x(1+ln(x))^2)