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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

(\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}}

Vereinfache

\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} (3 x^{2} + 6 x + 6)

\frac{d y}{d x} y = \frac{4 x}{3 x - 2 x ^{2}}

\frac{d}{d x} (1.4 x^{5} - 2.5 x^{2} + 6.7)

d er i v a t i v e x^{2} + 4

d er i v a t i v e y = (4 x + 3)^{10}