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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

y^{^{'}} = 0.002 y - 200

\int_{\frac{1}{2}}^{1} \frac{4 y + 5}{y ^{2} + y} d y

\int_{- 5}^{5} \frac{1}{x ^{(\frac{2}{3})}} d x

(0, - 3), (2, 1)

\frac{1}{3}

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