derivative (6x+x^2)/((3+x)^2)

Lösung

ableitung von

\frac{6 x + x ^{2}}{( 3 + x ) ^{2}}

\frac{18}{( 3 + x ) ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{6 x + x ^{2}}{( 3 + x ) ^{2}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 6 x + x ^{2} ) ( 3 + x ) ^{2} - \frac{d}{d x} ( ( 3 + x ) ^{2} ) ( 6 x + x ^{2} )}{( ( 3 + x ) ^{2} ) ^{2}}

\frac{d}{d x} (6 x + x^{2}) = 6 + 2 x

\frac{d}{d x} ((3 + x)^{2}) = 2 (3 + x)

= \frac{( 6 + 2 x ) ( 3 + x ) ^{2} - 2 ( 3 + x ) ( 6 x + x ^{2} )}{( ( 3 + x ) ^{2} ) ^{2}}

Vereinfache

\frac{( 6 + 2 x ) ( 3 + x ) ^{2} - 2 ( 3 + x ) ( 6 x + x ^{2} )}{( ( 3 + x ) ^{2} ) ^{2}} : \frac{18}{( 3 + x ) ^{3}}

= \frac{18}{( 3 + x ) ^{3}}

\frac{\partial}{\partial x} (e^{- 3 x^{2} - 2 y^{2}})

\int cos (x) sin (3 x) - 4 sin (x) d x

d er i v a t i v e \frac{( x + 11 )}{( x - 11 )}

2 x^{2} y + x^{3} \frac{d y}{d x} = 1

x \to 7 lim (e^{x - 7})