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}}

Graph

Popular Examples

limit as x approaches 4 of (|x-4|)/(4-x)

x \to 4 lim (\frac{∣ x - 4 ∣}{4 - x})

(\partial)/(\partial x)(2x+y-2)

\frac{\partial}{\partial x} (2 x + y - 2)

derivative of ae^x+b

\frac{d}{d x} (a e^{x} + b)

(\partial)/(\partial y)(xye^{-2y})

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

y^{'''}-2y^{''}-48y^'=0

y^{^{'''}} - 2 y^{^{''}} - 48 y^{^{'}} = 0

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)