What is the derivative of (5x^2+2x-6/(3x-1)) ?

The derivative of (5x^2+2x-6/(3x-1)) is (15x^2-10x+16)/((3x-1)^2)

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

The first derivative of (5x^2+2x-6/(3x-1)) is (15x^2-10x+16)/((3x-1)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (\frac{5 x ^{2} + 2 x - 6}{3 x - 1})

\frac{15 x ^{2} - 10 x + 16}{( 3 x - 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{5 x ^{2} + 2 x - 6}{3 x - 1})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 5 x ^{2} + 2 x - 6 ) ( 3 x - 1 ) - \frac{d}{d x} ( 3 x - 1 ) ( 5 x ^{2} + 2 x - 6 )}{( 3 x - 1 ) ^{2}}

\frac{d}{d x} (5 x^{2} + 2 x - 6) = 10 x + 2

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

= \frac{( 10 x + 2 ) ( 3 x - 1 ) - 3 ( 5 x ^{2} + 2 x - 6 )}{( 3 x - 1 ) ^{2}}

Expand

(10 x + 2) (3 x - 1) - 3 (5 x^{2} + 2 x - 6) : 15 x^{2} - 10 x + 16

= \frac{15 x ^{2} - 10 x + 16}{( 3 x - 1 ) ^{2}}

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

\frac{d}{d x} (ln (x) sin (x) cos (x))

f (x) = lo g_{2} (3 x)

f (x) = - 8.25 x^{2} + 66 x

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

What is the derivative of (5x^2+2x-6/(3x-1)) ?
The derivative of (5x^2+2x-6/(3x-1)) is (15x^2-10x+16)/((3x-1)^2)
What is the first derivative of (5x^2+2x-6/(3x-1)) ?
The first derivative of (5x^2+2x-6/(3x-1)) is (15x^2-10x+16)/((3x-1)^2)