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

Lösung

ableitung von

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

15 x^{4} + 24 x^{3} - 66 x^{2} + 8 x - 16

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d}{d x} (3 x^{3} + 2 x) = 9 x^{2} + 2

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

= (9 x^{2} + 2) (x - 2) (x + 4) + (2 x + 2) (3 x^{3} + 2 x)

Vereinfache

(9 x^{2} + 2) (x - 2) (x + 4) + (2 x + 2) (3 x^{3} + 2 x) : 15 x^{4} + 24 x^{3} - 66 x^{2} + 8 x - 16

= 15 x^{4} + 24 x^{3} - 66 x^{2} + 8 x - 16

cos (x) d x - sin (y) d y = 0

\int arcsin (d) x d x

n \to \infty lim (1 - n)

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

\frac{d y}{d x} = \frac{3 - y}{2 x}