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

Lösung

ableitung von

\frac{x ^{2}}{5 + x}

\frac{4 x ( 5 + x ) - x ^{\frac{3}{2}}}{2 ( 5 + x ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (5 + x) = \frac{1}{2 x}

= \frac{2 x ( 5 + x ) - \frac{1}{2 x} x ^{2}}{( 5 + x ) ^{2}}

Vereinfache

\frac{2 x ( 5 + x ) - \frac{1}{2 x} x ^{2}}{( 5 + x ) ^{2}} : \frac{4 x ( 5 + x ) - x ^{\frac{3}{2}}}{2 ( 5 + x ) ^{2}}

= \frac{4 x ( 5 + x ) - x ^{\frac{3}{2}}}{2 ( 5 + x ) ^{2}}

d er i v a t i v e - \frac{1}{( x - 1 ) ^{2}}

\int 2 sin (x) + cos (x) - 3 d x

\frac{d}{d y} (e^{- y})

in v erse l a pl a ce x^{\frac{1}{2}}

d er i v a t i v e y = 5 e^{(6 x + 7)}