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

The derivative of f(x)=((x+1)(2x-3))/(2x+3) is (4x^2+12x+3)/((2x+3)^2)

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

The first derivative of f(x)=((x+1)(2x-3))/(2x+3) is (4x^2+12x+3)/((2x+3)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

\frac{4 x ^{2} + 12 x + 3}{( 2 x + 3 ) ^{2}}

Solution steps

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

\frac{d}{d x} ((x + 1) (2 x - 3)) = 4 x - 1

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

= \frac{( 4 x - 1 ) ( 2 x + 3 ) - 2 ( x + 1 ) ( 2 x - 3 )}{( 2 x + 3 ) ^{2}}

Expand

(4 x - 1) (2 x + 3) - 2 (x + 1) (2 x - 3) : 4 x^{2} + 12 x + 3

= \frac{4 x ^{2} + 12 x + 3}{( 2 x + 3 ) ^{2}}

y^{^{''}} + 2 y^{^{'}} - 3 y = - 16 x e^{x}

y = 3 - x, y = 2 x^{2}, [0, 3]

\frac{d}{d x} (4 x + 2 y)

\frac{\partial}{\partial x} (- 6 x^{3} + y^{2} + 5 x y)

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

What is the derivative of f(x)=((x+1)(2x-3))/(2x+3) ?
The derivative of f(x)=((x+1)(2x-3))/(2x+3) is (4x^2+12x+3)/((2x+3)^2)
What is the first derivative of f(x)=((x+1)(2x-3))/(2x+3) ?
The first derivative of f(x)=((x+1)(2x-3))/(2x+3) is (4x^2+12x+3)/((2x+3)^2)