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

The derivative of f(x)= x/(x^2-x) is -1/((x-1)^2)

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

The first derivative of f(x)= x/(x^2-x) is -1/((x-1)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

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