derivative of sqrt((x^3/(2-x)))

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

\frac{1}{2 \frac{x ^{3}}{2 - x}} \frac{d}{d x} (\frac{x ^{3}}{2 - x})

= \frac{1}{2 \frac{x ^{3}}{2 - x}} \frac{d}{d x} (\frac{x ^{3}}{2 - x})

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

= \frac{1}{2 \frac{x ^{3}}{2 - x}} \cdot \frac{6 x ^{2} - 2 x ^{3}}{( 2 - x ) ^{2}}

Vereinfache

\frac{1}{2 \frac{x ^{3}}{2 - x}} \cdot \frac{6 x ^{2} - 2 x ^{3}}{( 2 - x ) ^{2}} : \frac{x ( - x + 3 )}{( - x + 2 ) ^{\frac{3}{2}}}

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