en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (5x+2)/(12x+5)

Solution

derivative of

\frac{5 x + 2}{12 x + 5}

Solution

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

Solution steps

\frac{d}{d x} (\frac{5 x + 2}{12 x + 5})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 5 x + 2 ) ( 12 x + 5 ) - \frac{d}{d x} ( 12 x + 5 ) ( 5 x + 2 )}{( 12 x + 5 ) ^{2}}

\frac{d}{d x} (5 x + 2) = 5

\frac{d}{d x} (12 x + 5) = 12

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

Expand

5 (12 x + 5) - 12 (5 x + 2) : 1

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

Popular Examples

integral of (sqrt(9x^2-1))/(x^2)

\int \frac{9 x ^{2} - 1}{x ^{2}} d x

derivative of (100/(x^2))

\frac{d}{d x} (\frac{100}{x ^{2}})

integral of (sin(2x))/(sqrt(sin^2(x)-3))

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

integral of (x^2e^{x^3})

\int (x^{2} e^{x^{3}}) d x

integral of arccos(2x)

\int arccos (2 x) d x

Frequently Asked Questions (FAQ)

What is the derivative of (5x+2)/(12x+5) ?
The derivative of (5x+2)/(12x+5) is 1/((12x+5)^2)
What is the first derivative of (5x+2)/(12x+5) ?
The first derivative of (5x+2)/(12x+5) is 1/((12x+5)^2)