What is the derivative of (sqrt(x)/(8x+8)) ?

The derivative of (sqrt(x)/(8x+8)) is -(x-1)/(16sqrt(x)(x+1)^2)

What is the first derivative of (sqrt(x)/(8x+8)) ?

The first derivative of (sqrt(x)/(8x+8)) is -(x-1)/(16sqrt(x)(x+1)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (\frac{x}{8 x + 8})

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

Solution steps

\frac{d}{d x} (\frac{x}{8 x + 8})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x) = \frac{1}{2 x}

\frac{d}{d x} (8 x + 8) = 8

= \frac{\frac{1}{2 x} ( 8 x + 8 ) - 8 x}{( 8 x + 8 ) ^{2}}

Simplify

\frac{\frac{1}{2 x} ( 8 x + 8 ) - 8 x}{( 8 x + 8 ) ^{2}} : - \frac{x - 1}{16 x ( x + 1 ) ^{2}}

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

What is the derivative of (sqrt(x)/(8x+8)) ?
The derivative of (sqrt(x)/(8x+8)) is -(x-1)/(16sqrt(x)(x+1)^2)
What is the first derivative of (sqrt(x)/(8x+8)) ?
The first derivative of (sqrt(x)/(8x+8)) is -(x-1)/(16sqrt(x)(x+1)^2)