derivative of 1/(\sqrt[3]{4x^2-7})

Lösung

\frac{d}{d x} (\frac{1}{3 4 x ^{2} - 7})

- \frac{8 x}{3 ( 4 x ^{2} - 7 ) ^{\frac{4}{3}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{3 4 x ^{2} - 7})

Wende Exponentenregel an:

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

= \frac{d}{d x} ((4 x^{2} - 7)^{- \frac{1}{3}})

Wende die Kettenregel an:

- \frac{1}{3 ( 4 x ^{2} - 7 ) ^{\frac{4}{3}}} \frac{d}{d x} (4 x^{2} - 7)

= - \frac{1}{3 ( 4 x ^{2} - 7 ) ^{\frac{4}{3}}} \frac{d}{d x} (4 x^{2} - 7)

\frac{d}{d x} (4 x^{2} - 7) = 8 x

= - \frac{1}{3 ( 4 x ^{2} - 7 ) ^{\frac{4}{3}}} \cdot 8 x

Vereinfache

- \frac{1}{3 ( 4 x ^{2} - 7 ) ^{\frac{4}{3}}} \cdot 8 x : - \frac{8 x}{3 ( 4 x ^{2} - 7 ) ^{\frac{4}{3}}}

= - \frac{8 x}{3 ( 4 x ^{2} - 7 ) ^{\frac{4}{3}}}

\frac{\partial}{\partial y} (- \frac{x}{y ^{2}})

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