derivative 9/((9-x^8)^{3/2)}

Lösung

ableitung von

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

\frac{108 x ^{7}}{( 9 - x ^{8} ) ^{\frac{5}{2}}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

- \frac{3}{2 ( 9 - x ^{8} ) ^{\frac{5}{2}}} \frac{d}{d x} (9 - x^{8})

= - \frac{3}{2 ( 9 - x ^{8} ) ^{\frac{5}{2}}} \frac{d}{d x} (9 - x^{8})

\frac{d}{d x} (9 - x^{8}) = - 8 x^{7}

= 9 (- \frac{3}{2 ( 9 - x ^{8} ) ^{\frac{5}{2}}} (- 8 x^{7}))

Vereinfache

9 (- \frac{3}{2 ( 9 - x ^{8} ) ^{\frac{5}{2}}} (- 8 x^{7})) : \frac{108 x ^{7}}{( 9 - x ^{8} ) ^{\frac{5}{2}}}

= \frac{108 x ^{7}}{( 9 - x ^{8} ) ^{\frac{5}{2}}}

\int_{3}^{5} \frac{x ^{2}}{8} d x

n = 1 \sum \infty \frac{n}{1000 n + 1}

d er i v a t i v e f (x) = \frac{1}{2}

\frac{d}{d x} (5 tan (x) sec (x))

x \to 9 lim (\frac{( x ^{2} - 4 x - 45 )}{x ^{2} - 81})