derivative of 1/(\sqrt[3]{8x^2})

Lösung

\frac{d}{d x} (\frac{1}{3 8 x ^{2}})

- \frac{1}{3 x ^{\frac{5}{3}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{3 8 x ^{2}})

Wende Exponentenregel an:

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

= \frac{d}{d x} ((8 x^{2})^{- \frac{1}{3}})

Wende die Kettenregel an:

- \frac{1}{3 ( 8 x ^{2} ) ^{\frac{4}{3}}} \frac{d}{d x} (8 x^{2})

= - \frac{1}{3 ( 8 x ^{2} ) ^{\frac{4}{3}}} \frac{d}{d x} (8 x^{2})

\frac{d}{d x} (8 x^{2}) = 16 x

= - \frac{1}{3 ( 8 x ^{2} ) ^{\frac{4}{3}}} \cdot 16 x

Vereinfache

- \frac{1}{3 ( 8 x ^{2} ) ^{\frac{4}{3}}} \cdot 16 x : - \frac{1}{3 x ^{\frac{5}{3}}}

= - \frac{1}{3 x ^{\frac{5}{3}}}

\int_{1}^{e} ln (8 x) d x

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

d er i v a t i v e f (x) = \frac{3 x + 2}{x + 1}

d er i v a t i v e \frac{1}{2} (6 t + 3)^{- \frac{1}{2}}

a re a x^{2} - 7 x - 26, - x^{2} + 3 x + 2