derivative of (x^2-3x^{-2/3}/x)

Lösung

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

\frac{x ^{\frac{8}{3}} + 5}{x ^{\frac{8}{3}}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (x^{2} - 3 x^{- \frac{2}{3}}) = \frac{2 + 2 x ^{\frac{8}{3}}}{x ^{\frac{5}{3}}}

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

= \frac{\frac{2 + 2 x ^{\frac{8}{3}}}{x ^{\frac{5}{3}}} x - 1 \cdot ( x ^{2} - 3 x ^{- \frac{2}{3}} )}{x ^{2}}

Vereinfache

\frac{\frac{2 + 2 x ^{\frac{8}{3}}}{x ^{\frac{5}{3}}} x - 1 \cdot ( x ^{2} - 3 x ^{- \frac{2}{3}} )}{x ^{2}} : \frac{x ^{\frac{8}{3}} + 5}{x ^{\frac{8}{3}}}

= \frac{x ^{\frac{8}{3}} + 5}{x ^{\frac{8}{3}}}

\int π (8.4 x - 2 x^{2})^{2} d x

\int tan^{6} (x) cos^{7} (x) d x

\int 1 7^{x} d x

\frac{d}{d x} (- \frac{0.4}{5 + 5 x})

x \to 4 lim ((f (x) g (x)) (x))