derivative of 1/(2x^{3/2})

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Potenzregel an:

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

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

Vereinfache

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

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

t a y l or x^{3}, 2

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

t an g e n t f (x) = x^{2} - 1, (- 4, 15)

d er i v a t i v e ln (x + 5)

\frac{d}{d x} (cos (\frac{nπ x}{2}))