What is the derivative of f(x)=(2x+6x^2)/((1+6x)^2) ?

The derivative of f(x)=(2x+6x^2)/((1+6x)^2) is 2/((1+6x)^3)

What is the first derivative of f(x)=(2x+6x^2)/((1+6x)^2) ?

The first derivative of f(x)=(2x+6x^2)/((1+6x)^2) is 2/((1+6x)^3)

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{2 x + 6 x ^{2}}{( 1 + 6 x ) ^{2}}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} ((1 + 6 x)^{2}) = 12 (1 + 6 x)

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

Simplify

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

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

\int \frac{x + 9}{x ^{2} + 8 x + 20} d x

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

\frac{d}{d t} (6 cos (2 t))

y = x^{3}, y = x^{2} - 9 x, [- 1, 1]

What is the derivative of f(x)=(2x+6x^2)/((1+6x)^2) ?
The derivative of f(x)=(2x+6x^2)/((1+6x)^2) is 2/((1+6x)^3)
What is the first derivative of f(x)=(2x+6x^2)/((1+6x)^2) ?
The first derivative of f(x)=(2x+6x^2)/((1+6x)^2) is 2/((1+6x)^3)