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

Lösung

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

\frac{8 x ^{2} - 40 x + 32}{3 x ^{\frac{1}{3}}}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

Vereinfache

\frac{2}{3 x ^{\frac{1}{3}}} (x - 4)^{2} + 2 (x - 4) x^{\frac{2}{3}} : \frac{8 x ^{2} - 40 x + 32}{3 x ^{\frac{1}{3}}}

= \frac{8 x ^{2} - 40 x + 32}{3 x ^{\frac{1}{3}}}

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

x \to c lim (x^{2} + a)

d er i v a t i v e \frac{1}{8 x}

\int (3 x + 5) e^{(3 x + 5)} d x

d er i v a t i v e y = 2 e^{x} + \frac{8}{3 x}