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

The derivative of (2-x^2)/((2+x^2)^2) is -(2x(-x^2+6))/((x^2+2)^3)

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

The first derivative of (2-x^2)/((2+x^2)^2) is -(2x(-x^2+6))/((x^2+2)^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

- \frac{2 x ( - x ^{2} + 6 )}{( x ^{2} + 2 ) ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{( - 2 x ) ( 2 + x ^{2} ) ^{2} - 4 x ( 2 + x ^{2} ) ( 2 - x ^{2} )}{( ( 2 + x ^{2} ) ^{2} ) ^{2}} : - \frac{2 x ( - x ^{2} + 6 )}{( x ^{2} + 2 ) ^{3}}

= - \frac{2 x ( - x ^{2} + 6 )}{( x ^{2} + 2 ) ^{3}}

\frac{d}{d x} (4 x^{3} ln (x))

f (x) = 110 x - 16 x^{2}, at x = 3.438

\int 6 cos (7 x) d x

e^{s i n (x^{2})}

x \to - \infty lim (\frac{2 x ^{2} + 3}{2 x + 3})

What is the derivative of (2-x^2)/((2+x^2)^2) ?
The derivative of (2-x^2)/((2+x^2)^2) is -(2x(-x^2+6))/((x^2+2)^3)
What is the first derivative of (2-x^2)/((2+x^2)^2) ?
The first derivative of (2-x^2)/((2+x^2)^2) is -(2x(-x^2+6))/((x^2+2)^3)