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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int sec (x) (cos (x) + tan (x)) d x

\frac{1}{1 + s + s ^{2}}

\frac{d}{d x} (5 x sin (x) cos (x))

\int (3 - x) d x

\int_{0}^{l n (π)} 2 x e^{x^{2}} cos (e^{x^{2}}) d x

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