derivative of 8(x-3^{2/3})

Lösung

\frac{d}{d x} (8 (x - 3)^{\frac{2}{3}})

\frac{16}{3 ( x - 3 ) ^{\frac{1}{3}}}

Schritte zur Lösung

\frac{d}{d x} (8 (x - 3)^{\frac{2}{3}})

Entferne die Konstante:

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

= 8 \frac{d}{d x} ((x - 3)^{\frac{2}{3}})

Wende die Kettenregel an:

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

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

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

= 8 \cdot \frac{2}{3 ( x - 3 ) ^{\frac{1}{3}}} \cdot 1

Vereinfache

8 \cdot \frac{2}{3 ( x - 3 ) ^{\frac{1}{3}}} \cdot 1 : \frac{16}{3 ( x - 3 ) ^{\frac{1}{3}}}

= \frac{16}{3 ( x - 3 ) ^{\frac{1}{3}}}

\int_{0}^{1} x + 9 d x

\frac{\partial}{\partial x} (e^{- r x})

d er i v a t i v e \frac{3}{x + 7}

\int 0.2 x^{2} + 1 d x

d er i v a t i v e 3 x^{2} (x^{2} + 1)