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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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