What is the derivative of (3x+2/(x-1)) ?

The derivative of (3x+2/(x-1)) is -5/((x-1)^2)

What is the first derivative of (3x+2/(x-1)) ?

The first derivative of (3x+2/(x-1)) is -5/((x-1)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (\frac{3 x + 2}{x - 1})

- \frac{5}{( x - 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 x + 2}{x - 1})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 3 x + 2 ) ( x - 1 ) - \frac{d}{d x} ( x - 1 ) ( 3 x + 2 )}{( x - 1 ) ^{2}}

\frac{d}{d x} (3 x + 2) = 3

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

= \frac{3 ( x - 1 ) - 1 \cdot ( 3 x + 2 )}{( x - 1 ) ^{2}}

Simplify

\frac{3 ( x - 1 ) - 1 \cdot ( 3 x + 2 )}{( x - 1 ) ^{2}} : - \frac{5}{( x - 1 ) ^{2}}

= - \frac{5}{( x - 1 ) ^{2}}

\frac{d}{d x} (\frac{e ^{x}}{x + 1})

\int \frac{e ^{\frac{x}{2}}}{2} d x

n = 0 \sum \infty (- \frac{5}{8})^{n}

lo g_{e} (\frac{1}{csc ( x )})

(1 + x)^{\frac{1}{x}}

What is the derivative of (3x+2/(x-1)) ?
The derivative of (3x+2/(x-1)) is -5/((x-1)^2)
What is the first derivative of (3x+2/(x-1)) ?
The first derivative of (3x+2/(x-1)) is -5/((x-1)^2)