derivative of 8/5 x^{-2/4}

Lösung

\frac{d}{d x} (\frac{8}{5} x^{- \frac{2}{4}})

- \frac{4}{5 x ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{8}{5} x^{- \frac{2}{4}})

Entferne die Konstante:

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

= \frac{8}{5} \frac{d}{d x} (x^{- \frac{2}{4}})

Wende die Potenzregel an:

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

= \frac{8}{5} (- \frac{2}{4} x^{- \frac{2}{4} - 1})

Vereinfache

\frac{8}{5} (- \frac{2}{4} x^{- \frac{2}{4} - 1}) : - \frac{4}{5 x ^{\frac{3}{2}}}

= - \frac{4}{5 x ^{\frac{3}{2}}}

t an g e n t f (x) = x^{3} + 2 x, at x = 3

x \to 1 lim (7)

ma c l a u r in x^{4}

a re a v (t) = t - 13, [0, 3]

a re a 2 x^{3} + 10 x^{2} + 22 x - 3, x^{3} - x^{2} - 6 x - 3, - 2, - 2