en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (x-4/(x+2))

Solution

\frac{d}{d x} (\frac{x - 4}{x + 2})

Solution

\frac{6}{( x + 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x - 4}{x + 2})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x - 4 ) ( x + 2 ) - \frac{d}{d x} ( x + 2 ) ( x - 4 )}{( x + 2 ) ^{2}}

\frac{d}{d x} (x - 4) = 1

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

= \frac{1 \cdot ( x + 2 ) - 1 \cdot ( x - 4 )}{( x + 2 ) ^{2}}

Simplify

\frac{1 \cdot ( x + 2 ) - 1 \cdot ( x - 4 )}{( x + 2 ) ^{2}} : \frac{6}{( x + 2 ) ^{2}}

= \frac{6}{( x + 2 ) ^{2}}

Popular Examples

limit as x approaches 3 of 4x^2-2x+10

x \to 3 lim (4 x^{2} - 2 x + 10)

integral of 8e^x

\int 8 e^{x} d x

derivative of (x+2/(x-4))

\frac{d}{d x} (\frac{x + 2}{x - 4})

derivative of-2ab^2e^{-b^2x^2}x derivative of

- 2 a b^{2} e^{- b^{2} x^{2}} x

derivative of (x^3e^{(3x)})

\frac{d}{d x} ((x)^{3} e^{(3 x)})

Frequently Asked Questions (FAQ)

What is the derivative of (x-4/(x+2)) ?
The derivative of (x-4/(x+2)) is 6/((x+2)^2)
What is the first derivative of (x-4/(x+2)) ?
The first derivative of (x-4/(x+2)) is 6/((x+2)^2)