derivative f(x)= 1/(sqrt(x^3))

Lösung

ableitung von

f (x) = \frac{1}{x ^{3}}

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

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{x ^{3}})

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

d er i v a t i v e f (x) = - \frac{10}{x}, at x = - 12

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

d er i v a t i v e f (x) = \frac{1}{x ^{3}}

p o l a r (- 1, 1)

d er i v a t i v e f (x) = 9 x + 5, at x = 7