derivative of 2/(9x^{5/3})

Lösung

\frac{d}{d x} (\frac{2}{9 x ^{\frac{5}{3}}})

- \frac{10}{27 x ^{\frac{8}{3}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2}{9 x ^{\frac{5}{3}}})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{2}{9} \frac{d}{d x} (\frac{1}{x ^{\frac{5}{3}}})

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

= \frac{2}{9} \frac{d}{d x} (x^{- \frac{5}{3}})

Wende die Potenzregel an:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{2}{9} (- \frac{5}{3} x^{- \frac{5}{3} - 1})

Vereinfache

\frac{2}{9} (- \frac{5}{3} x^{- \frac{5}{3} - 1}) : - \frac{10}{27 x ^{\frac{8}{3}}}

= - \frac{10}{27 x ^{\frac{8}{3}}}

a re a y^{2} = x + 6, y^{2} = 2 - x

\frac{d}{d x} (4 cos (3 x))

l a pl a ce t r an s f or m - 7 (t - 4)

\frac{d}{d x} (x (2 x + 1)^{5})

\frac{d y}{d x} = 5 y + y^{2}