What is the derivative of (10x+8x^2/((5+8x)^2)) ?

The derivative of (10x+8x^2/((5+8x)^2)) is (50)/((5+8x)^3)

What is the first derivative of (10x+8x^2/((5+8x)^2)) ?

The first derivative of (10x+8x^2/((5+8x)^2)) is (50)/((5+8x)^3)

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{10 x + 8 x ^{2}}{( 5 + 8 x ) ^{2}})

\frac{50}{( 5 + 8 x ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{10 x + 8 x ^{2}}{( 5 + 8 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 + 8 x ^{2} ) ( 5 + 8 x ) ^{2} - \frac{d}{d x} ( ( 5 + 8 x ) ^{2} ) ( 10 x + 8 x ^{2} )}{( ( 5 + 8 x ) ^{2} ) ^{2}}

\frac{d}{d x} (10 x + 8 x^{2}) = 10 + 16 x

\frac{d}{d x} ((5 + 8 x)^{2}) = 16 (5 + 8 x)

= \frac{( 10 + 16 x ) ( 5 + 8 x ) ^{2} - 16 ( 5 + 8 x ) ( 10 x + 8 x ^{2} )}{( ( 5 + 8 x ) ^{2} ) ^{2}}

Simplify

\frac{( 10 + 16 x ) ( 5 + 8 x ) ^{2} - 16 ( 5 + 8 x ) ( 10 x + 8 x ^{2} )}{( ( 5 + 8 x ) ^{2} ) ^{2}} : \frac{50}{( 5 + 8 x ) ^{3}}

= \frac{50}{( 5 + 8 x ) ^{3}}

\frac{s}{s + 1}

\int \frac{1}{5} - \frac{7}{x} d x

\int_{\frac{π}{2}}^{\infty} \frac{7}{x} d x

\int \frac{1}{2 + sin ( x )} d x

\frac{d}{d x} (3 cos (x))

What is the derivative of (10x+8x^2/((5+8x)^2)) ?
The derivative of (10x+8x^2/((5+8x)^2)) is (50)/((5+8x)^3)
What is the first derivative of (10x+8x^2/((5+8x)^2)) ?
The first derivative of (10x+8x^2/((5+8x)^2)) is (50)/((5+8x)^3)