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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} ((3 x^{2} - 1)^{2}) = 12 x (3 x^{2} - 1)

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

= \frac{12 x ( 3 x ^{2} - 1 ) ( x + 1 ) ^{3} - 3 ( x + 1 ) ^{2} ( 3 x ^{2} - 1 ) ^{2}}{( ( x + 1 ) ^{3} ) ^{2}}

Simplify

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

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

d er i v a t i v e 1 4^{x} + 16

d er i v a t i v e \frac{2 x - 3}{x}

d er i v a t i v e y = x + 2 sin (x) + 2

d er i v a t i v e x^{\frac{1}{2}} + x^{2}

d er i v a t i v e sin^{2} (3 x - 2)

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