What is the derivative of (-2x^2+8/(sqrt(8-x^2))) ?

The derivative of (-2x^2+8/(sqrt(8-x^2))) is (2x^3-24x)/((8-x^2)sqrt(8-x^2))

What is the first derivative of (-2x^2+8/(sqrt(8-x^2))) ?

The first derivative of (-2x^2+8/(sqrt(8-x^2))) is (2x^3-24x)/((8-x^2)sqrt(8-x^2))

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\frac{d}{d x} (\frac{- 2 x ^{2} + 8}{8 - x ^{2}})

\frac{2 x ^{3} - 24 x}{( 8 - x ^{2} ) 8 - x ^{2}}

Solution steps

\frac{d}{d x} (\frac{- 2 x ^{2} + 8}{8 - x ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( - 2 x ^{2} + 8 ) 8 - x ^{2} - \frac{d}{d x} ( 8 - x ^{2} ) ( - 2 x ^{2} + 8 )}{( 8 - x ^{2} ) ^{2}}

\frac{d}{d x} (- 2 x^{2} + 8) = - 4 x

\frac{d}{d x} (8 - x^{2}) = - \frac{x}{8 - x ^{2}}

= \frac{( - 4 x ) 8 - x ^{2} - ( - \frac{x}{8 - x ^{2}} ) ( - 2 x ^{2} + 8 )}{( 8 - x ^{2} ) ^{2}}

Simplify

\frac{( - 4 x ) 8 - x ^{2} - ( - \frac{x}{8 - x ^{2}} ) ( - 2 x ^{2} + 8 )}{( 8 - x ^{2} ) ^{2}} : \frac{2 x ^{3} - 24 x}{( 8 - x ^{2} ) 8 - x ^{2}}

= \frac{2 x ^{3} - 24 x}{( 8 - x ^{2} ) 8 - x ^{2}}

\int_{0}^{\frac{π}{6}} sec (x) d x

x \to - 1 lim (\frac{1}{- x - 1})

\int (2 x^{2} - 4 x)^{9} (x - 1) d x

\int 8 x^{3} + 30 x - 1 d x

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

What is the derivative of (-2x^2+8/(sqrt(8-x^2))) ?
The derivative of (-2x^2+8/(sqrt(8-x^2))) is (2x^3-24x)/((8-x^2)sqrt(8-x^2))
What is the first derivative of (-2x^2+8/(sqrt(8-x^2))) ?
The first derivative of (-2x^2+8/(sqrt(8-x^2))) is (2x^3-24x)/((8-x^2)sqrt(8-x^2))