What is the derivative of (x^2/(8-8x)) ?

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

What is the first derivative of (x^2/(8-8x)) ?

The first derivative of (x^2/(8-8x)) is (x(-x+2))/(8(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 ^{2}}{8 - 8 x})

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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