derivative 1/(sqrt(x^5))

Lösung

ableitung von

\frac{1}{x ^{5}}

- \frac{5 x ^{4}}{2 ( x ^{5} ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{x ^{5}})

Wende Exponentenregel an:

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

= \frac{d}{d x} ((x^{5})^{- \frac{1}{2}})

Wende die Kettenregel an:

- \frac{1}{2 ( x ^{5} ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{5})

= - \frac{1}{2 ( x ^{5} ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{5})

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

= - \frac{1}{2 ( x ^{5} ) ^{\frac{3}{2}}} \cdot 5 x^{4}

Vereinfache

- \frac{1}{2 ( x ^{5} ) ^{\frac{3}{2}}} \cdot 5 x^{4} : - \frac{5 x ^{4}}{2 ( x ^{5} ) ^{\frac{3}{2}}}

= - \frac{5 x ^{4}}{2 ( x ^{5} ) ^{\frac{3}{2}}}

\int - sec^{2} (x) + cos (2 x) d x

d er i v a t i v e \frac{( 5 x - 2 )}{( x ^{2} + 1 )}

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

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

(5 y^{2} - x y) d x + x^{2} d y = 0