derivative of 2x^{-3}+sqrt(x)-8x+15

Lösung

\frac{d}{d x} (2 x^{- 3} + x - 8 x + 15)

\frac{x ^{\frac{7}{2}} - 12}{2 x ^{\frac{7}{2}} x} - 8

Schritte zur Lösung

\frac{d}{d x} (2 x^{- 3} + x - 8 x + 15)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (2 x^{- 3}) + \frac{d}{d x} (x) - \frac{d}{d x} (8 x) + \frac{d}{d x} (15)

\frac{d}{d x} (2 x^{- 3}) = - \frac{6}{x ^{4}}

\frac{d}{d x} (x) = \frac{1}{2 x}

\frac{d}{d x} (8 x) = 8

\frac{d}{d x} (15) = 0

= - \frac{6}{x ^{4}} + \frac{1}{2 x} - 8 + 0

Vereinfache

- \frac{6}{x ^{4}} + \frac{1}{2 x} - 8 + 0 : \frac{x ^{\frac{7}{2}} - 12}{2 x ^{\frac{7}{2}} x} - 8

= \frac{x ^{\frac{7}{2}} - 12}{2 x ^{\frac{7}{2}} x} - 8

y^{^{''}} + 4 y = cos (2 x) + sin (2 x)

n = 0 \sum \infty x^{3 n}

\int 24 e^{20 t} d t

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

x \to - 3 - lim (\frac{2}{x ^{2} - 9})