derivative f(x)=(x^2)/(2+sqrt(x))

Lösung

ableitung von

f (x) = \frac{x ^{2}}{2 + x}

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (2 + x) = \frac{1}{2 x}

= \frac{2 x ( 2 + x ) - \frac{1}{2 x} x ^{2}}{( 2 + x ) ^{2}}

Vereinfache

\frac{2 x ( 2 + x ) - \frac{1}{2 x} x ^{2}}{( 2 + x ) ^{2}} : \frac{4 x ( 2 + x ) - x ^{\frac{3}{2}}}{2 ( 2 + x ) ^{2}}

= \frac{4 x ( 2 + x ) - x ^{\frac{3}{2}}}{2 ( 2 + x ) ^{2}}

n \to \infty lim (\frac{n}{1})

\int e^{3 x} cos (4 x) d x

\frac{d}{d x} (x^{\frac{l n ( 2 )}{1 + l n ( x )}})

\int \frac{7}{( t - 1 ) t ^{2} - 2 t - 48} d t

n = 0 \sum \infty 3^{n - 1}