What is the derivative of (4x-6/(x-6)) ?

The derivative of (4x-6/(x-6)) is -(18)/((x-6)^2)

What is the first derivative of (4x-6/(x-6)) ?

The first derivative of (4x-6/(x-6)) is -(18)/((x-6)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (\frac{4 x - 6}{x - 6})

- \frac{18}{( x - 6 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 x - 6}{x - 6})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 4 x - 6 ) ( x - 6 ) - \frac{d}{d x} ( x - 6 ) ( 4 x - 6 )}{( x - 6 ) ^{2}}

\frac{d}{d x} (4 x - 6) = 4

\frac{d}{d x} (x - 6) = 1

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

Simplify

\frac{4 ( x - 6 ) - 1 \cdot ( 4 x - 6 )}{( x - 6 ) ^{2}} : - \frac{18}{( x - 6 ) ^{2}}

= - \frac{18}{( x - 6 ) ^{2}}

What is the derivative of (4x-6/(x-6)) ?
The derivative of (4x-6/(x-6)) is -(18)/((x-6)^2)
What is the first derivative of (4x-6/(x-6)) ?
The first derivative of (4x-6/(x-6)) is -(18)/((x-6)^2)