What is the derivative of ((x-1)/x)^2 ?

The derivative of ((x-1)/x)^2 is (2(x-1))/(x^3)

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

The first derivative of ((x-1)/x)^2 is (2(x-1))/(x^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

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

\frac{2 ( x - 1 )}{x ^{3}}

Solution steps

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

Apply the chain rule:

2 \cdot \frac{x - 1}{x} \frac{d}{d x} (\frac{x - 1}{x})

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

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

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

Simplify

2 \cdot \frac{x - 1}{x} \cdot \frac{1}{x ^{2}} : \frac{2 ( x - 1 )}{x ^{3}}

= \frac{2 ( x - 1 )}{x ^{3}}

What is the derivative of ((x-1)/x)^2 ?
The derivative of ((x-1)/x)^2 is (2(x-1))/(x^3)
What is the first derivative of ((x-1)/x)^2 ?
The first derivative of ((x-1)/x)^2 is (2(x-1))/(x^3)