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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\frac{d}{d x} (\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}}

6 x^{2} + 3 x y + y^{2} = 16, (1, 2)

\int_{1}^{8} π (x - 1)^{2} d x

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

\int \frac{1}{e ^{2 x} + 4} d x

y^{^{''}} + 4 y^{^{'}} + 3 y = e^{- 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)