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

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

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

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

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derivative of

\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{5 x}{x + 4} (1.1)

y^{^{''}} + 5 y^{^{'}} = e^{- t}

y^{^{'}} + y cos (x) = 2 cos (x)

y = \frac{10}{x ^{2} - 2 x - 24}, x = - 2, x = 2

h^{^{'}} = 6 - 5 cos (\frac{π}{15} t)

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