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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\frac{d}{d 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}}

\int e^{2 x} (1 - 2 e^{2 x})^{2} d x

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

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

\int e^{6 x} sin (x) d x

f (x) = 1.5 x^{7} - \frac{x ^{4}}{3} + π x - e x^{2} + 2

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)