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

The derivative of (-x^2-9/((x^2-9)^2)) is -(2x(-x^2-27))/((x^2-9)^3)

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

The first derivative of (-x^2-9/((x^2-9)^2)) is -(2x(-x^2-27))/((x^2-9)^3)

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

- \frac{2 x ( - x ^{2} - 27 )}{( x ^{2} - 9 ) ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} ((x^{2} - 9)^{2}) = 4 x (x^{2} - 9)

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

Simplify

\frac{( - 2 x ) ( x ^{2} - 9 ) ^{2} - 4 x ( x ^{2} - 9 ) ( - x ^{2} - 9 )}{( ( x ^{2} - 9 ) ^{2} ) ^{2}} : - \frac{2 x ( - x ^{2} - 27 )}{( x ^{2} - 9 ) ^{3}}

= - \frac{2 x ( - x ^{2} - 27 )}{( x ^{2} - 9 ) ^{3}}

\frac{d}{d x} (\frac{x ^{2}}{5 + 4 x})

(x^{2} + 1) y^{^{'}} + 4 x (y - 1) = 0, y (0) = 5

\int x 16 - 25 x^{2} d x

\int_{0}^{\frac{π}{2}} 3 cos (x) d x

f (x) = (3 x^{3} + 2 x) (x - 2) (x + 4)

What is the derivative of (-x^2-9/((x^2-9)^2)) ?
The derivative of (-x^2-9/((x^2-9)^2)) is -(2x(-x^2-27))/((x^2-9)^3)
What is the first derivative of (-x^2-9/((x^2-9)^2)) ?
The first derivative of (-x^2-9/((x^2-9)^2)) is -(2x(-x^2-27))/((x^2-9)^3)