derivative of 20x^{-8}+5x^{-3}-7x^{-7}

Lösung

\frac{d}{d x} (20 x^{- 8} + 5 x^{- 3} - 7 x^{- 7})

- \frac{160}{x ^{9}} - \frac{15}{x ^{4}} + \frac{49}{x ^{8}}

Schritte zur Lösung

\frac{d}{d x} (20 x^{- 8} + 5 x^{- 3} - 7 x^{- 7})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (20 x^{- 8}) + \frac{d}{d x} (5 x^{- 3}) - \frac{d}{d x} (7 x^{- 7})

\frac{d}{d x} (20 x^{- 8}) = - \frac{160}{x ^{9}}

\frac{d}{d x} (5 x^{- 3}) = - \frac{15}{x ^{4}}

\frac{d}{d x} (7 x^{- 7}) = - \frac{49}{x ^{8}}

= - \frac{160}{x ^{9}} - \frac{15}{x ^{4}} - (- \frac{49}{x ^{8}})

Vereinfache

= - \frac{160}{x ^{9}} - \frac{15}{x ^{4}} + \frac{49}{x ^{8}}

\frac{d}{d x} (\frac{1}{x ^{2} - 9 y ^{2}})

\frac{d}{d x} ((1 - x^{2})^{10})

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

s l o p e (- \frac{2}{7}, \frac{2}{3}), (\frac{5}{7}, - \frac{7}{3})

x \to 1 lim (\frac{x - 1}{x ^{n} - 1})