derivative of x/((x-1^{2/3)(x+2)^{1/3}})

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (x^{2} y^{4} e^{y} - x^{2} y^{2} - 3 x)

\int sec^{4} (9 x) d x

y^{^{'}} = cos (y - x + 3)

\int 7 tan (7 x) d x

\int 3 tan (x) d x