What is the derivative of (10x+2x^2)/((5+2x)^2) ?

The derivative of (10x+2x^2)/((5+2x)^2) is (50)/((5+2x)^3)

What is the first derivative of (10x+2x^2)/((5+2x)^2) ?

The first derivative of (10x+2x^2)/((5+2x)^2) is (50)/((5+2x)^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{10 x + 2 x ^{2}}{( 5 + 2 x ) ^{2}}

\frac{50}{( 5 + 2 x ) ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (10 x + 2 x^{2}) = 10 + 4 x

\frac{d}{d x} ((5 + 2 x)^{2}) = 4 (5 + 2 x)

= \frac{( 10 + 4 x ) ( 5 + 2 x ) ^{2} - 4 ( 5 + 2 x ) ( 10 x + 2 x ^{2} )}{( ( 5 + 2 x ) ^{2} ) ^{2}}

Simplify

\frac{( 10 + 4 x ) ( 5 + 2 x ) ^{2} - 4 ( 5 + 2 x ) ( 10 x + 2 x ^{2} )}{( ( 5 + 2 x ) ^{2} ) ^{2}} : \frac{50}{( 5 + 2 x ) ^{3}}

= \frac{50}{( 5 + 2 x ) ^{3}}

\frac{d y}{d t} + a y + b = 0

n = 0 \sum \infty (\frac{9}{10})^{n}

\int \frac{1 - w}{w} d w

\int - e^{- x} d x

What is the derivative of (10x+2x^2)/((5+2x)^2) ?
The derivative of (10x+2x^2)/((5+2x)^2) is (50)/((5+2x)^3)
What is the first derivative of (10x+2x^2)/((5+2x)^2) ?
The first derivative of (10x+2x^2)/((5+2x)^2) is (50)/((5+2x)^3)