derivative of 1/(5x^{4/5})

Lösung

\frac{d}{d x} (\frac{1}{5 x ^{\frac{4}{5}}})

- \frac{4}{25 x ^{\frac{9}{5}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{5 x ^{\frac{4}{5}}})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{5} \frac{d}{d x} (\frac{1}{x ^{\frac{4}{5}}})

Wende Exponentenregel an:

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

= \frac{1}{5} \frac{d}{d x} (x^{- \frac{4}{5}})

Wende die Potenzregel an:

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

= \frac{1}{5} (- \frac{4}{5} x^{- \frac{4}{5} - 1})

Vereinfache

\frac{1}{5} (- \frac{4}{5} x^{- \frac{4}{5} - 1}) : - \frac{4}{25 x ^{\frac{9}{5}}}

= - \frac{4}{25 x ^{\frac{9}{5}}}

\int w d w

\int x^{3} + 2 x d x

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

t an g e n t f (x) = - 8 x^{2} + 5 x, at x = - 1

\int 5 x + c d x