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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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

\frac{d}{d θ} (e^{2 θ})

\int \frac{1}{x ( ln ( x ^{2} ) )} d x

\int x^{4} a x^{5} - b d x

\frac{\partial}{\partial x} (ln (x + 6 y + 9 z))