derivative f(x)=-x^{2/3}(x-5)

Lösung

ableitung von

f (x) = - x^{\frac{2}{3}} (x - 5)

- \frac{5 x - 10}{3 x ^{\frac{1}{3}}}

Schritte zur Lösung

\frac{d}{d x} (- x^{\frac{2}{3}} (x - 5))

Entferne die Konstante:

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

= - \frac{d}{d x} (x^{\frac{2}{3}} (x - 5))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{\frac{2}{3}}, g = x - 5

= - (\frac{d}{d x} (x^{\frac{2}{3}}) (x - 5) + \frac{d}{d x} (x - 5) x^{\frac{2}{3}})

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

\frac{d}{d x} (x - 5) = 1

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

Vereinfache

- (\frac{2}{3 x ^{\frac{1}{3}}} (x - 5) + 1 \cdot x^{\frac{2}{3}}) : - \frac{5 x - 10}{3 x ^{\frac{1}{3}}}

= - \frac{5 x - 10}{3 x ^{\frac{1}{3}}}

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

\int x^{\frac{1}{2}} + 6 d x

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

x \to 0 lim (\frac{e ^{x}}{ln ( x )})

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