derivative of (-2x^2+9/(sqrt(9-x^2)))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

y^{^{'}} = (y + 2 t)^{2}, y (0) = 3

\frac{\partial}{\partial x} (x^{7} - 6 x y - 3 y^{2})

\int (sin (\frac{x}{2}) + cos (\frac{x}{2}))^{2} d x

in v erse l a pl a ce \frac{2 ( s + 1 )}{s ( s ^{2} + s + 2 )}

n = 1 \sum \infty \frac{4}{( n + 1 ) !}