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

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

in v erse l a pl a ce \frac{2}{s ^{2}} \cdot e^{- s}

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

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

\frac{d}{d x} (3 x^{2} - 12 x + 9)

11 t^{2} y^{^{''}} - 22 y = 9 t^{2} - 9