en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (ln(x)/x)

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

(dy)/(dx)=(((2y+7))/(8x+9))^2

\frac{d y}{d x} = (\frac{( 2 y + 7 )}{8 x + 9})^{2}

integral from 0 to 2 of (6ti-t^3j+5t^9k)

\int_{0}^{2} (6 t i - t^{3} j + 5 t^{9} k) d t

limit as x approaches 0 of (x+5)/(3x)

x \to 0 lim (\frac{x + 5}{3 x})

(\partial)/(\partial x)((e^{x/2})(2xy))

\frac{\partial}{\partial x} ((e^{\frac{x}{2}}) (2 x y))

derivative of (x^2)/(x-9)derivative of

\frac{x ^{2}}{x - 9}

Frequently Asked Questions (FAQ)

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