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Beliebt Rechnen >

derivative f(x)=sqrt(1/(x^{31))}

Lösung

ableitung von

f (x) = \frac{1}{x ^{31}}

Lösung

- \frac{31 x ^{30}}{2 x ^{\frac{63}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{x ^{31}})

Wende die Kettenregel an:

\frac{1}{2 \frac{1}{x ^{31}}} \frac{d}{d x} (\frac{1}{x ^{31}})

= \frac{1}{2 \frac{1}{x ^{31}}} \frac{d}{d x} (\frac{1}{x ^{31}})

\frac{d}{d x} (\frac{1}{x ^{31}}) = - \frac{31}{x ^{32}}

= \frac{1}{2 \frac{1}{x ^{31}}} (- \frac{31}{x ^{32}})

Vereinfache

\frac{1}{2 \frac{1}{x ^{31}}} (- \frac{31}{x ^{32}}) : - \frac{31 x ^{30}}{2 x ^{\frac{63}{2}}}

= - \frac{31 x ^{30}}{2 x ^{\frac{63}{2}}}

Graph

Beliebte Beispiele

derivative of ln(3^{x^2})

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

limit as x approaches 4 of 3x^3-2x^2+x-7

x \to 4 lim (3 x^{3} - 2 x^{2} + x - 7)

derivative ((3x^2))/4+x/3

d er i v a t i v e \frac{( 3 x ^{2} )}{4} + \frac{x}{3}

integral of (3-18x)/(sqrt(25-9x^2))

\int \frac{3 - 18 x}{25 - 9 x ^{2}} d x

derivative ln((4x)/(x+7))

d er i v a t i v e ln (\frac{4 x}{x + 7})