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

The derivative of (x^2)/(3(2-x)) is (4x-x^2)/(3(2-x)^2)

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

The first derivative of (x^2)/(3(2-x)) is (4x-x^2)/(3(2-x)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

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

\frac{4 x - x ^{2}}{3 ( 2 - x ) ^{2}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{1}{3} \cdot \frac{2 x ( 2 - x ) - ( - 1 ) x ^{2}}{( 2 - x ) ^{2}} : \frac{4 x - x ^{2}}{3 ( 2 - x ) ^{2}}

= \frac{4 x - x ^{2}}{3 ( 2 - x ) ^{2}}

What is the derivative of (x^2)/(3(2-x)) ?
The derivative of (x^2)/(3(2-x)) is (4x-x^2)/(3(2-x)^2)
What is the first derivative of (x^2)/(3(2-x)) ?
The first derivative of (x^2)/(3(2-x)) is (4x-x^2)/(3(2-x)^2)