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

Lösung

ableitung von

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

14 x^{6} - 16 x^{3} - 16

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d}{d x} (2 x^{3} + 4) = 6 x^{2}

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

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

Vereinfache

6 x^{2} (x^{4} - 4 x) + (4 x^{3} - 4) (2 x^{3} + 4) : 14 x^{6} - 16 x^{3} - 16

= 14 x^{6} - 16 x^{3} - 16

d er i v a t i v e \frac{6}{x ^{3}} - \frac{6}{x ^{2}} - \frac{1}{x} + 350

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

\frac{d}{d x} (2 x + 2 x ln (x))

t an g e n t (4 x + 4)^{\frac{1}{3}}, at x = 2

t an g e n t y = \frac{- 6 x}{x ^{2} + 1}, (- 1, 3)