derivative (-u^2+7)/((u^2+7)^2)

Lösung

ableitung von

\frac{- u ^{2} + 7}{( u ^{2} + 7 ) ^{2}}

- \frac{2 u ( - u ^{2} + 21 )}{( u ^{2} + 7 ) ^{3}}

Schritte zur Lösung

\frac{d}{d u} (\frac{- u ^{2} + 7}{( u ^{2} + 7 ) ^{2}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d u} ( - u ^{2} + 7 ) ( u ^{2} + 7 ) ^{2} - \frac{d}{d u} ( ( u ^{2} + 7 ) ^{2} ) ( - u ^{2} + 7 )}{( ( u ^{2} + 7 ) ^{2} ) ^{2}}

\frac{d}{d u} (- u^{2} + 7) = - 2 u

\frac{d}{d u} ((u^{2} + 7)^{2}) = 4 u (u^{2} + 7)

= \frac{( - 2 u ) ( u ^{2} + 7 ) ^{2} - 4 u ( u ^{2} + 7 ) ( - u ^{2} + 7 )}{( ( u ^{2} + 7 ) ^{2} ) ^{2}}

Vereinfache

\frac{( - 2 u ) ( u ^{2} + 7 ) ^{2} - 4 u ( u ^{2} + 7 ) ( - u ^{2} + 7 )}{( ( u ^{2} + 7 ) ^{2} ) ^{2}} : - \frac{2 u ( - u ^{2} + 21 )}{( u ^{2} + 7 ) ^{3}}

= - \frac{2 u ( - u ^{2} + 21 )}{( u ^{2} + 7 ) ^{3}}

\frac{d}{d x} (sec (x^{5} + x))

s l o p e in t erce pt (1.1) (0.5)

\int 1 + 5 x^{2} (10 x) d x

d er i v a t i v e y = 3 x^{2} + \frac{10 x}{3} - 2

\frac{d}{d x} (\frac{tan ^{3} ( x )}{3})