derivative of (9x^{5/2}-2/x)

Lösung

\frac{d}{d x} (\frac{9 x ^{\frac{5}{2}} - 2}{x})

\frac{27 x ^{\frac{5}{2}} + 4}{2 x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{9 x ^{\frac{5}{2}} - 2}{x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 9 x ^{\frac{5}{2}} - 2 ) x - \frac{d x}{d x} ( 9 x ^{\frac{5}{2}} - 2 )}{x ^{2}}

\frac{d}{d x} (9 x^{\frac{5}{2}} - 2) = \frac{45 x ^{\frac{3}{2}}}{2}

\frac{d x}{d x} = 1

= \frac{\frac{45 x ^{\frac{3}{2}}}{2} x - 1 \cdot ( 9 x ^{\frac{5}{2}} - 2 )}{x ^{2}}

Vereinfache

\frac{\frac{45 x ^{\frac{3}{2}}}{2} x - 1 \cdot ( 9 x ^{\frac{5}{2}} - 2 )}{x ^{2}} : \frac{27 x ^{\frac{5}{2}} + 4}{2 x ^{2}}

= \frac{27 x ^{\frac{5}{2}} + 4}{2 x ^{2}}