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

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

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

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

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{x ^{2} - 2 x + 2}{x - 1})

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int 1 + 4 y^{2} d y

\frac{ln ( x )}{x ^{3}}

y = \frac{5 x ^{2} + 3}{x ^{2} + 1}

\frac{\partial}{\partial x} (cos (\frac{x}{2}))

x \to 7 lim (2 x^{- 1})

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