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

Lösung

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

\frac{5 x - 8}{3 x ^{\frac{1}{3}}}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{\frac{2}{3}}, g = x - 4

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

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

\frac{d}{d x} (x - 4) = 1

= \frac{2}{3 x ^{\frac{1}{3}}} (x - 4) + 1 \cdot x^{\frac{2}{3}}

Vereinfache

\frac{2}{3 x ^{\frac{1}{3}}} (x - 4) + 1 \cdot x^{\frac{2}{3}} : \frac{5 x - 8}{3 x ^{\frac{1}{3}}}

= \frac{5 x - 8}{3 x ^{\frac{1}{3}}}

\frac{d}{d x} ((2 x - 8)^{5})

l a pl a ce t r an s f or m f (t) = t^{2} e^{3 t}

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

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

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