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

Lösung

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

- \frac{1}{3 x ^{\frac{4}{3}}}

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Potenzregel an:

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

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

Vereinfache

- \frac{1}{3} x^{- \frac{1}{3} - 1} : - \frac{1}{3 x ^{\frac{4}{3}}}

= - \frac{1}{3 x ^{\frac{4}{3}}}

\frac{\partial}{\partial x} (a sin (x) sin (y))

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

\frac{\partial}{\partial x} (\frac{2 s - 3 t}{3 s + 5 t})

\int \frac{1}{( x ^{2} + 9 ) ^{3}} d x

d er i v a t i v e (x^{4} + 5 x^{2} - 5)^{4}