derivative f(x)=(6x+5)(x^3-2)

Lösung

ableitung von

f (x) = (6 x + 5) (x^{3} - 2)

24 x^{3} + 15 x^{2} - 12

Schritte zur Lösung

\frac{d}{d x} ((6 x + 5) (x^{3} - 2))

Wende die Produktregel an:

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

f = 6 x + 5, g = x^{3} - 2

= \frac{d}{d x} (6 x + 5) (x^{3} - 2) + \frac{d}{d x} (x^{3} - 2) (6 x + 5)

\frac{d}{d x} (6 x + 5) = 6

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

= 6 (x^{3} - 2) + 3 x^{2} (6 x + 5)

Vereinfache

6 (x^{3} - 2) + 3 x^{2} (6 x + 5) : 24 x^{3} + 15 x^{2} - 12

= 24 x^{3} + 15 x^{2} - 12

x \to 0 lim (x^{3} sin (x))

d er i v a t i v e f (x) = x^{4} - 12 x^{3} + 3

\int 8 sin^{3} (x) cos (x) d x

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

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