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

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int 3 x^{2} y + 4 x y^{2} d x

\int 7 tan (8 x) sec^{2} (8 x) d x

\int x + 6 d x

\int t ln (t) d t

\frac{\partial}{\partial x} (ln (x^{2} - y^{2}))