en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (2x-3/(2x+3))

Solution

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

Solution

\frac{12}{( 2 x + 3 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

2 (2 x + 3) - 2 (2 x - 3) : 12

= \frac{12}{( 2 x + 3 ) ^{2}}

Popular Examples

y^{'''}+y^{''}-y^'-y=4e^x

y^{^{'''}} + y^{^{''}} - y^{^{'}} - y = 4 e^{x}

derivative of sin^2(x-3)

\frac{d}{d x} (sin^{2} (x) - 3)

(\partial)/(\partial x)(e^{5x}cos(7y))

\frac{\partial}{\partial x} (e^{5 x} cos (7 y))

derivative of (2x+3/(5x+4))

\frac{d}{d x} (\frac{2 x + 3}{5 x + 4})

derivative of 2e^{(x-5})

\frac{d}{d x} (2 e^{(x - 5)})

Frequently Asked Questions (FAQ)

What is the derivative of (2x-3/(2x+3)) ?
The derivative of (2x-3/(2x+3)) is (12)/((2x+3)^2)
What is the first derivative of (2x-3/(2x+3)) ?
The first derivative of (2x-3/(2x+3)) is (12)/((2x+3)^2)