What is the derivative of (2x-3/(3x+4)) ?

The derivative of (2x-3/(3x+4)) is (17)/((3x+4)^2)

What is the first derivative of (2x-3/(3x+4)) ?

The first derivative of (2x-3/(3x+4)) is (17)/((3x+4)^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{2 x - 3}{3 x + 4})

\frac{17}{( 3 x + 4 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x - 3}{3 x + 4})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 2 x - 3 ) ( 3 x + 4 ) - \frac{d}{d x} ( 3 x + 4 ) ( 2 x - 3 )}{( 3 x + 4 ) ^{2}}

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

\frac{d}{d x} (3 x + 4) = 3

= \frac{2 ( 3 x + 4 ) - 3 ( 2 x - 3 )}{( 3 x + 4 ) ^{2}}

Expand

2 (3 x + 4) - 3 (2 x - 3) : 17

= \frac{17}{( 3 x + 4 ) ^{2}}

What is the derivative of (2x-3/(3x+4)) ?
The derivative of (2x-3/(3x+4)) is (17)/((3x+4)^2)
What is the first derivative of (2x-3/(3x+4)) ?
The first derivative of (2x-3/(3x+4)) is (17)/((3x+4)^2)