What is the derivative of ((6x^2-11x+2))/((3x-1)) ?

The derivative of ((6x^2-11x+2))/((3x-1)) is (18x^2-12x+5)/((3x-1)^2)

What is the first derivative of ((6x^2-11x+2))/((3x-1)) ?

The first derivative of ((6x^2-11x+2))/((3x-1)) is (18x^2-12x+5)/((3x-1)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{( 6 x ^{2} - 11 x + 2 )}{( 3 x - 1 )}

\frac{18 x ^{2} - 12 x + 5}{( 3 x - 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{6 x ^{2} - 11 x + 2}{3 x - 1})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 6 x ^{2} - 11 x + 2 ) ( 3 x - 1 ) - \frac{d}{d x} ( 3 x - 1 ) ( 6 x ^{2} - 11 x + 2 )}{( 3 x - 1 ) ^{2}}

\frac{d}{d x} (6 x^{2} - 11 x + 2) = 12 x - 11

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

= \frac{( 12 x - 11 ) ( 3 x - 1 ) - 3 ( 6 x ^{2} - 11 x + 2 )}{( 3 x - 1 ) ^{2}}

Expand

(12 x - 11) (3 x - 1) - 3 (6 x^{2} - 11 x + 2) : 18 x^{2} - 12 x + 5

= \frac{18 x ^{2} - 12 x + 5}{( 3 x - 1 ) ^{2}}

\int (ln^{2} (x)) d x

\frac{d}{d x} (cos (y) \cdot \frac{d y}{d x})

n = 2 \sum \infty \frac{1}{( n - 1 ) ^{2}}

\frac{x}{e ^{x}}

\frac{d y}{d x} = e^{5 x + 6 y}

What is the derivative of ((6x^2-11x+2))/((3x-1)) ?
The derivative of ((6x^2-11x+2))/((3x-1)) is (18x^2-12x+5)/((3x-1)^2)
What is the first derivative of ((6x^2-11x+2))/((3x-1)) ?
The first derivative of ((6x^2-11x+2))/((3x-1)) is (18x^2-12x+5)/((3x-1)^2)