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

Lösung

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

\frac{x ^{\frac{1}{2}}}{2}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Vereinfache

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

= \frac{x ^{\frac{1}{2}}}{2}

\int_{0}^{1} (1 - x^{3})^{2} d x

d er i v a t i v e g (x) = ln (2 x^{2} + 4)

d er i v a t i v e (6 t - 1) (4 t - 4)^{- 1}

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

\int 2 x (x^{2} + 10)^{3} d x