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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int_{1}^{9} \frac{x - 2}{x} d x

x \to 0 lim (\frac{x}{x ^{2} + 2 x})

\int_{0}^{2} x 7 - x^{2} d x

(11, 6), (16, y)

\frac{\partial}{\partial y} (y (e^{x} - 1))

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