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

The derivative of (2x^2/(4-x^2)) is (16x)/((4-x^2)^2)

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

The first derivative of (2x^2/(4-x^2)) is (16x)/((4-x^2)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

\frac{16 x}{( 4 - x ^{2} ) ^{2}}

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

2 \cdot \frac{2 x ( 4 - x ^{2} ) - ( - 2 x ) x ^{2}}{( 4 - x ^{2} ) ^{2}} : \frac{16 x}{( 4 - x ^{2} ) ^{2}}

= \frac{16 x}{( 4 - x ^{2} ) ^{2}}

What is the derivative of (2x^2/(4-x^2)) ?
The derivative of (2x^2/(4-x^2)) is (16x)/((4-x^2)^2)
What is the first derivative of (2x^2/(4-x^2)) ?
The first derivative of (2x^2/(4-x^2)) is (16x)/((4-x^2)^2)