derivative of (6^{2/3}-x^{2/3}^{3/2})

Lösung

\frac{d}{d x} ((6^{\frac{2}{3}} - x^{\frac{2}{3}})^{\frac{3}{2}})

- \frac{( 6 ^{\frac{2}{3}} - x ^{\frac{2}{3}} ) ^{\frac{1}{2}}}{x ^{\frac{1}{3}}}

Schritte zur Lösung

\frac{d}{d x} ((6^{\frac{2}{3}} - x^{\frac{2}{3}})^{\frac{3}{2}})

Wende die Kettenregel an:

\frac{3 ( 6 ^{\frac{2}{3}} - x ^{\frac{2}{3}} ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (6^{\frac{2}{3}} - x^{\frac{2}{3}})

= \frac{3 ( 6 ^{\frac{2}{3}} - x ^{\frac{2}{3}} ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (6^{\frac{2}{3}} - x^{\frac{2}{3}})

\frac{d}{d x} (6^{\frac{2}{3}} - x^{\frac{2}{3}}) = - \frac{2}{3 x ^{\frac{1}{3}}}

= \frac{3 ( 6 ^{\frac{2}{3}} - x ^{\frac{2}{3}} ) ^{\frac{1}{2}}}{2} (- \frac{2}{3 x ^{\frac{1}{3}}})

Vereinfache

\frac{3 ( 6 ^{\frac{2}{3}} - x ^{\frac{2}{3}} ) ^{\frac{1}{2}}}{2} (- \frac{2}{3 x ^{\frac{1}{3}}}) : - \frac{( 6 ^{\frac{2}{3}} - x ^{\frac{2}{3}} ) ^{\frac{1}{2}}}{x ^{\frac{1}{3}}}

= - \frac{( 6 ^{\frac{2}{3}} - x ^{\frac{2}{3}} ) ^{\frac{1}{2}}}{x ^{\frac{1}{3}}}

\int \frac{1}{x ^{2} + x + 5} d x

\int e^{3 x - 2} d x

\frac{d y}{d x} - 9 y^{2} e^{- 1 x} = 0, y (0) = 5

t an g e n t y = x^{4}, at x = 0

in v erse l a pl a ce cos (5 t)