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Beliebt Rechnen >

derivative of 1/(x*sqrt(x))

Lösung

\frac{d}{d x} (\frac{1}{x \cdot x})

Lösung

- \frac{3}{2 x ^{\frac{5}{2}}}

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= - \frac{3}{2 x ^{\frac{5}{2}}}

Graph

Beliebte Beispiele

integral of 2t^3

\int 2 t^{3} d t

integral of 2/(xsqrt(x^2+1))

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

integral of e^{6x}sin(6x)

\int e^{6 x} sin (6 x) d x

(dy)/(dx)-y^2=0

\frac{d y}{d x} - y^{2} = 0

derivative of (x^4/(2-x^3))

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