derivative of 40x(5x^2-8)

Lösung

\frac{d}{d x} (40 x (5 x^{2} - 8))

40 (15 x^{2} - 8)

Schritte zur Lösung

\frac{d}{d x} (40 x (5 x^{2} - 8))

Entferne die Konstante:

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

= 40 \frac{d}{d x} (x (5 x^{2} - 8))

Wende die Produktregel an:

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

f = x, g = 5 x^{2} - 8

= 40 (\frac{d x}{d x} (5 x^{2} - 8) + \frac{d}{d x} (5 x^{2} - 8) x)

\frac{d x}{d x} = 1

\frac{d}{d x} (5 x^{2} - 8) = 10 x

= 40 (1 \cdot (5 x^{2} - 8) + 10 xx)

Vereinfache

40 (1 \cdot (5 x^{2} - 8) + 10 xx) : 40 (15 x^{2} - 8)

= 40 (15 x^{2} - 8)

\int_{2}^{\infty} \frac{1}{x ^{5}} d x

\int x e^{\frac{x ^{2}}{2}} d x

x \to π lim (3 arctan (x))

d er i v a t i v e \frac{x ^{2} - 1}{x + 3}

\frac{\partial}{\partial y} (x^{3})