derivative of 2/3 x^2(x^3-1)

Lösung

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

\frac{2 ( 5 x ^{4} - 2 x )}{3}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x^{2}, g = x^{3} - 1

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

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

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

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

Vereinfache

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

= \frac{2 ( 5 x ^{4} - 2 x )}{3}

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

\int \frac{cos ( x )}{9 - sin ( x )} d x

\frac{d}{d x} (3 x (10 x^{3} - \frac{6}{x + 10}))

\frac{d}{d x} (- 5 cos (5 x))

x \to - \infty lim (5^{x} + 2)