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

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

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

The first derivative of (-x^2-2/((x^2-2)^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 >

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

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

Solution steps

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

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

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

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

Simplify

\frac{( - 2 x ) ( x ^{2} - 2 ) ^{2} - 4 x ( x ^{2} - 2 ) ( - x ^{2} - 2 )}{( ( x ^{2} - 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} (\frac{1 - cos ( x )}{x})

\int \frac{2 x - 1}{2 x + 3} d x

\frac{d}{d x} (ln (x + 2 y + 3 z))

y^{^{'''}} = e^{- 0.2 x}

\frac{( s + 2 )}{( s ^{2} + 4 )}

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