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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

Vereinfache

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

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

ma c l a u r in e^{- 3 x^{2}}

x \to 6 lim (f (x) - g (x))

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

in v erse l a pl a ce \frac{1}{s ^{2} - 4}

(x sin (2 π x))^{^{'}}