derivative (-u^2+5)/((u^2+5)^2)

Lösung

ableitung von

\frac{- u ^{2} + 5}{( u ^{2} + 5 ) ^{2}}

- \frac{2 u ( - u ^{2} + 15 )}{( u ^{2} + 5 ) ^{3}}

Schritte zur Lösung

\frac{d}{d u} (\frac{- u ^{2} + 5}{( u ^{2} + 5 ) ^{2}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d u} ( - u ^{2} + 5 ) ( u ^{2} + 5 ) ^{2} - \frac{d}{d u} ( ( u ^{2} + 5 ) ^{2} ) ( - u ^{2} + 5 )}{( ( u ^{2} + 5 ) ^{2} ) ^{2}}

\frac{d}{d u} (- u^{2} + 5) = - 2 u

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

= \frac{( - 2 u ) ( u ^{2} + 5 ) ^{2} - 4 u ( u ^{2} + 5 ) ( - u ^{2} + 5 )}{( ( u ^{2} + 5 ) ^{2} ) ^{2}}

Vereinfache

\frac{( - 2 u ) ( u ^{2} + 5 ) ^{2} - 4 u ( u ^{2} + 5 ) ( - u ^{2} + 5 )}{( ( u ^{2} + 5 ) ^{2} ) ^{2}} : - \frac{2 u ( - u ^{2} + 15 )}{( u ^{2} + 5 ) ^{3}}

= - \frac{2 u ( - u ^{2} + 15 )}{( u ^{2} + 5 ) ^{3}}

\int ln (9 x + 7) d x

d er i v a t i v e f (x) = (2 x^{2} - 3)^{2}

\int_{1}^{3} (3 x^{2} + 5 x - 4) d x

in v erse l a pl a ce s - 1

\int e^{- x} cos (x) d x