derivative of (4-x^{2/3}^{2/3})

Lösung

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

- \frac{4}{9 x ^{\frac{1}{3}} ( 4 - x ^{\frac{2}{3}} ) ^{\frac{1}{3}}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{2}{3 ( 4 - x ^{\frac{2}{3}} ) ^{\frac{1}{3}}} (- \frac{2}{3 x ^{\frac{1}{3}}}) : - \frac{4}{9 x ^{\frac{1}{3}} ( 4 - x ^{\frac{2}{3}} ) ^{\frac{1}{3}}}

= - \frac{4}{9 x ^{\frac{1}{3}} ( 4 - x ^{\frac{2}{3}} ) ^{\frac{1}{3}}}

\int \frac{x - 11}{x ^{2} + 6 x + 25} d x

\int \frac{x ^{2} - 7 x + 12}{x - 3} d x

d er i v a t i v e y = \frac{3 x - 9}{2 x + 8}

\frac{d}{d x} (\frac{4 + ln ( 2 x )}{2020 + x})

t a y l or e^{4 x}, 3