derivative of 9/(sqrt(x+8))

Lösung

\frac{d}{d x} (\frac{9}{x + 8})

- \frac{9}{2 ( x + 8 ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{9}{x + 8})

Entferne die Konstante:

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

= 9 \frac{d}{d x} (\frac{1}{x + 8})

Wende Exponentenregel an:

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

= 9 \frac{d}{d x} ((x + 8)^{- \frac{1}{2}})

Wende die Kettenregel an:

- \frac{1}{2 ( x + 8 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 8)

= - \frac{1}{2 ( x + 8 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 8)

\frac{d}{d x} (x + 8) = 1

= 9 (- \frac{1}{2 ( x + 8 ) ^{\frac{3}{2}}} \cdot 1)

Vereinfache

9 (- \frac{1}{2 ( x + 8 ) ^{\frac{3}{2}}} \cdot 1) : - \frac{9}{2 ( x + 8 ) ^{\frac{3}{2}}}

= - \frac{9}{2 ( x + 8 ) ^{\frac{3}{2}}}

t an g e n t f (x) = 2 x^{3} + 7 x, at x = 1

\frac{d}{d x} (- 19 e^{x})

\int arcsin (2 x) d x

\int cos (4 x) (1 - sin (4 x))^{3} d x

x \to - 3 lim (\frac{x ^{2} - 8}{3 - x})