What is (\partial)/(\partial x)(x/((1-x)^2)) ?

The answer to (\partial)/(\partial x)(x/((1-x)^2)) is (1+x)/((1-x)^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(x/((1-x)^2))

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{\partial}{\partial x} (x) = 1

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

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

Simplify

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

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

What is (\partial)/(\partial x)(x/((1-x)^2)) ?
The answer to (\partial)/(\partial x)(x/((1-x)^2)) is (1+x)/((1-x)^3)