derivative (8x+x^2)/((4+x)^2)

Lösung

ableitung von

\frac{8 x + x ^{2}}{( 4 + x ) ^{2}}

\frac{32}{( 4 + x ) ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{8 x + x ^{2}}{( 4 + x ) ^{2}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 8 x + x ^{2} ) ( 4 + x ) ^{2} - \frac{d}{d x} ( ( 4 + x ) ^{2} ) ( 8 x + x ^{2} )}{( ( 4 + x ) ^{2} ) ^{2}}

\frac{d}{d x} (8 x + x^{2}) = 8 + 2 x

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

= \frac{( 8 + 2 x ) ( 4 + x ) ^{2} - 2 ( 4 + x ) ( 8 x + x ^{2} )}{( ( 4 + x ) ^{2} ) ^{2}}

Vereinfache

\frac{( 8 + 2 x ) ( 4 + x ) ^{2} - 2 ( 4 + x ) ( 8 x + x ^{2} )}{( ( 4 + x ) ^{2} ) ^{2}} : \frac{32}{( 4 + x ) ^{3}}

= \frac{32}{( 4 + x ) ^{3}}

\int \frac{x}{4 - 5 x ^{2}} d x

d er i v a t i v e f (x) = \frac{x}{x + 5}

t an g e n t 6 cos (x)

y^{^{''}} + 16 y = - 32 sec (4 t)

\int 3 y^{2} - 2 x d y