d/(dl)((dl^2-d-al^3-bl^2)/(l^2))

Lösung

\frac{d}{d l} (\frac{d l ^{2} - d - a l ^{3} - b l ^{2}}{l ^{2}})

\frac{- a l ^{3} + 2 d}{l ^{3}}

Schritte zur Lösung

\frac{d}{d l} (\frac{d l ^{2} - d - a l ^{3} - b l ^{2}}{l ^{2}})

Behandle

a, b, d

als Konstante

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d l} ( d l ^{2} - d - a l ^{3} - b l ^{2} ) l ^{2} - \frac{d}{d l} ( l ^{2} ) ( d l ^{2} - d - a l ^{3} - b l ^{2} )}{( l ^{2} ) ^{2}}

\frac{d}{d l} (d l^{2} - d - a l^{3} - b l^{2}) = - 3 a l^{2} + 2 d l - 2 b l

\frac{d}{d l} (l^{2}) = 2 l

= \frac{( - 3 a l ^{2} + 2 d l - 2 b l ) l ^{2} - 2 l ( d l ^{2} - d - a l ^{3} - b l ^{2} )}{( l ^{2} ) ^{2}}

Vereinfache

\frac{( - 3 a l ^{2} + 2 d l - 2 b l ) l ^{2} - 2 l ( d l ^{2} - d - a l ^{3} - b l ^{2} )}{( l ^{2} ) ^{2}} : \frac{- a l ^{3} + 2 d}{l ^{3}}

= \frac{- a l ^{3} + 2 d}{l ^{3}}

\int \frac{sin ( 2 x )}{( 1 - cos ^{2} ( x ) ) ^{3}} d x

d er i v a t i v e 17 e^{x}

\frac{\partial}{\partial t} (e^{- t})

\int cos (3 x) sin (x) d x

\int p (p + 9)^{8} d p