What is the derivative of f(x)=(-x^2-6)/((x^2-6)^2) ?

The derivative of f(x)=(-x^2-6)/((x^2-6)^2) is -(2x(-x^2-18))/((x^2-6)^3)

What is the first derivative of f(x)=(-x^2-6)/((x^2-6)^2) ?

The first derivative of f(x)=(-x^2-6)/((x^2-6)^2) is -(2x(-x^2-18))/((x^2-6)^3)

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derivative of

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

- \frac{2 x ( - x ^{2} - 18 )}{( x ^{2} - 6 ) ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} ((x^{2} - 6)^{2}) = 4 x (x^{2} - 6)

= \frac{( - 2 x ) ( x ^{2} - 6 ) ^{2} - 4 x ( x ^{2} - 6 ) ( - x ^{2} - 6 )}{( ( x ^{2} - 6 ) ^{2} ) ^{2}}

Simplify

\frac{( - 2 x ) ( x ^{2} - 6 ) ^{2} - 4 x ( x ^{2} - 6 ) ( - x ^{2} - 6 )}{( ( x ^{2} - 6 ) ^{2} ) ^{2}} : - \frac{2 x ( - x ^{2} - 18 )}{( x ^{2} - 6 ) ^{3}}

= - \frac{2 x ( - x ^{2} - 18 )}{( x ^{2} - 6 ) ^{3}}

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

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

y = (5 - x^{2})^{5}

\int x^{2} + 6 x + 13 d x

f (x) = \frac{1}{x ^{3}}, at x = 1

What is the derivative of f(x)=(-x^2-6)/((x^2-6)^2) ?
The derivative of f(x)=(-x^2-6)/((x^2-6)^2) is -(2x(-x^2-18))/((x^2-6)^3)
What is the first derivative of f(x)=(-x^2-6)/((x^2-6)^2) ?
The first derivative of f(x)=(-x^2-6)/((x^2-6)^2) is -(2x(-x^2-18))/((x^2-6)^3)