en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (x-2/x)

Solution

\frac{d}{d x} (\frac{x - 2}{x})

Solution

\frac{2}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{x - 2}{x})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= \frac{2}{x ^{2}}

Popular Examples

derivative of (3x/(2y))

\frac{d}{d x} (\frac{3 x}{2 y})

integral of x^3sqrt(1+9x^2)

\int x^{3} 1 + 9 x^{2} d x

integral of 1+3x^2

\int 1 + 3 x^{2} d x

limit as x approaches 0 of (e^x+e^{-x}-2)/(xsin(x))

x \to 0 lim (\frac{e ^{x} + e ^{- x} - 2}{x sin ( x )})

integral of 1/(x^2+8x+65)

\int \frac{1}{x ^{2} + 8 x + 65} d x

Frequently Asked Questions (FAQ)

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