derivative f(x)=(2x^3+3)(x^4-2x)

Lösung

ableitung von

f (x) = (2 x^{3} + 3) (x^{4} - 2 x)

14 x^{6} - 4 x^{3} - 6

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d}{d x} (2 x^{3} + 3) = 6 x^{2}

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

= 6 x^{2} (x^{4} - 2 x) + (4 x^{3} - 2) (2 x^{3} + 3)

Vereinfache

6 x^{2} (x^{4} - 2 x) + (4 x^{3} - 2) (2 x^{3} + 3) : 14 x^{6} - 4 x^{3} - 6

= 14 x^{6} - 4 x^{3} - 6

x \to \infty lim (∣ x + 1 ∣)

a re a y = 11 x^{2}, y = x^{2} + 7

n = 1 \sum \infty (1 + \frac{2}{n})^{2} e^{- 5 n}

d er i v a t i v e 5 x^{2} - 1 + 7 e^{x}

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