derivative y= 1/(\sqrt[3]{x-1)}

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

\int (cos^{3} (x) sin (x)) d x

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

(x^{2} + y^{2}) d x + (2 x y) d y = 0

y^{^{'}} = \frac{x ^{2} - y ^{2}}{x y}, y (2) = 5

\frac{\partial}{\partial y} (e^{x y z^{4}} y z^{4})