derivative (10x+x^2)/((5+x)^2)

Lösung

ableitung von

\frac{10 x + x ^{2}}{( 5 + x ) ^{2}}

\frac{50}{( 5 + x ) ^{3}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 10 x + x ^{2} ) ( 5 + x ) ^{2} - \frac{d}{d x} ( ( 5 + x ) ^{2} ) ( 10 x + x ^{2} )}{( ( 5 + x ) ^{2} ) ^{2}}

\frac{d}{d x} (10 x + x^{2}) = 10 + 2 x

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

= \frac{( 10 + 2 x ) ( 5 + x ) ^{2} - 2 ( 5 + x ) ( 10 x + x ^{2} )}{( ( 5 + x ) ^{2} ) ^{2}}

Vereinfache

\frac{( 10 + 2 x ) ( 5 + x ) ^{2} - 2 ( 5 + x ) ( 10 x + x ^{2} )}{( ( 5 + x ) ^{2} ) ^{2}} : \frac{50}{( 5 + x ) ^{3}}

= \frac{50}{( 5 + x ) ^{3}}

\int e^{x} 2 + e^{x} d x

\int \frac{x ^{3}}{( 4 x ^{2} + 9 ) ^{\frac{3}{2}}} d x

d er i v a t i v e \frac{1}{7 - 10 e ^{x}}

\frac{d}{d x} (\frac{ln ( x + 1 )}{ln ( x - 1 )})

d er i v a t i v e x^{2} e^{- 3 x}