What is the derivative of y=(2x+5)/(3x-2) ?

The derivative of y=(2x+5)/(3x-2) is -(19)/((3x-2)^2)

What is the first derivative of y=(2x+5)/(3x-2) ?

The first derivative of y=(2x+5)/(3x-2) is -(19)/((3x-2)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

y = \frac{2 x + 5}{3 x - 2}

- \frac{19}{( 3 x - 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x + 5}{3 x - 2})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 2 x + 5 ) ( 3 x - 2 ) - \frac{d}{d x} ( 3 x - 2 ) ( 2 x + 5 )}{( 3 x - 2 ) ^{2}}

\frac{d}{d x} (2 x + 5) = 2

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

= \frac{2 ( 3 x - 2 ) - 3 ( 2 x + 5 )}{( 3 x - 2 ) ^{2}}

Simplify

\frac{2 ( 3 x - 2 ) - 3 ( 2 x + 5 )}{( 3 x - 2 ) ^{2}} : - \frac{19}{( 3 x - 2 ) ^{2}}

= - \frac{19}{( 3 x - 2 ) ^{2}}

What is the derivative of y=(2x+5)/(3x-2) ?
The derivative of y=(2x+5)/(3x-2) is -(19)/((3x-2)^2)
What is the first derivative of y=(2x+5)/(3x-2) ?
The first derivative of y=(2x+5)/(3x-2) is -(19)/((3x-2)^2)