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

The derivative of (-x^2-3)/((x^2-3)^2) is -(2x(-x^2-9))/((x^2-3)^3)

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

The first derivative of (-x^2-3)/((x^2-3)^2) is -(2x(-x^2-9))/((x^2-3)^3)

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derivative of

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

- \frac{2 x ( - x ^{2} - 9 )}{( x ^{2} - 3 ) ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} ((x^{2} - 3)^{2}) = 4 x (x^{2} - 3)

= \frac{( - 2 x ) ( x ^{2} - 3 ) ^{2} - 4 x ( x ^{2} - 3 ) ( - x ^{2} - 3 )}{( ( x ^{2} - 3 ) ^{2} ) ^{2}}

Simplify

\frac{( - 2 x ) ( x ^{2} - 3 ) ^{2} - 4 x ( x ^{2} - 3 ) ( - x ^{2} - 3 )}{( ( x ^{2} - 3 ) ^{2} ) ^{2}} : - \frac{2 x ( - x ^{2} - 9 )}{( x ^{2} - 3 ) ^{3}}

= - \frac{2 x ( - x ^{2} - 9 )}{( x ^{2} - 3 ) ^{3}}

\frac{d ^{2}}{d x ^{2}} (3 x^{- 3} + 5 x^{2})

\int \frac{x}{( 2 x + 1 ) ^{3}} d x

\frac{d x}{x - x ^{2}} = 3 d t

\frac{\partial}{\partial y} (14 - x^{2} - 4 y^{2})

x \to 2 lim (\frac{x ^{2} + 1}{x})

What is the derivative of (-x^2-3)/((x^2-3)^2) ?
The derivative of (-x^2-3)/((x^2-3)^2) is -(2x(-x^2-9))/((x^2-3)^3)
What is the first derivative of (-x^2-3)/((x^2-3)^2) ?
The first derivative of (-x^2-3)/((x^2-3)^2) is -(2x(-x^2-9))/((x^2-3)^3)