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

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

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

The first derivative of ((x^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} )}{x - 1})

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

Solution steps

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

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

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

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

Simplify

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

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

x \to 0 lim (\frac{x ^{2} - 4 x}{x})

x \to 7 + lim (\frac{x - 7}{∣ x - 7 ∣})

\int t^{\frac{3}{2}} d t

\frac{d v}{d t} = 9.8 - k v

\int 3 csc^{2} (x) - 5 sec (x) tan (x) d x

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