What is the derivative of (x^2)/(5(1-x)) ?

The derivative of (x^2)/(5(1-x)) is (2x-x^2)/(5(1-x)^2)

What is the first derivative of (x^2)/(5(1-x)) ?

The first derivative of (x^2)/(5(1-x)) is (2x-x^2)/(5(1-x)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{x ^{2}}{5 ( 1 - x )}

\frac{2 x - x ^{2}}{5 ( 1 - x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{5 ( 1 - x )})

Take the constant out:

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

= \frac{1}{5} \frac{d}{d x} (\frac{x ^{2}}{1 - x})

Apply the Quotient Rule:

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

= \frac{1}{5} \cdot \frac{\frac{d}{d x} ( x ^{2} ) ( 1 - x ) - \frac{d}{d x} ( 1 - x ) x ^{2}}{( 1 - x ) ^{2}}

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

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

= \frac{1}{5} \cdot \frac{2 x ( 1 - x ) - ( - 1 ) x ^{2}}{( 1 - x ) ^{2}}

Simplify

\frac{1}{5} \cdot \frac{2 x ( 1 - x ) - ( - 1 ) x ^{2}}{( 1 - x ) ^{2}} : \frac{2 x - x ^{2}}{5 ( 1 - x ) ^{2}}

= \frac{2 x - x ^{2}}{5 ( 1 - x ) ^{2}}

f (x) = 2 x^{2} + x - 1, at a = - 1

\int 9 sin (3 x) d x

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

f (x) = x^{\frac{4}{3}}

\int_{2 π}^{\infty} sin (x) d x

What is the derivative of (x^2)/(5(1-x)) ?
The derivative of (x^2)/(5(1-x)) is (2x-x^2)/(5(1-x)^2)
What is the first derivative of (x^2)/(5(1-x)) ?
The first derivative of (x^2)/(5(1-x)) is (2x-x^2)/(5(1-x)^2)