derivative (5x+2)(x^3+4x)

Lösung

ableitung von

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

20 x^{3} + 6 x^{2} + 40 x + 8

Schritte zur Lösung

\frac{d}{d x} ((5 x + 2) (x^{3} + 4 x))

Wende die Produktregel an:

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

f = 5 x + 2, g = x^{3} + 4 x

= \frac{d}{d x} (5 x + 2) (x^{3} + 4 x) + \frac{d}{d x} (x^{3} + 4 x) (5 x + 2)

\frac{d}{d x} (5 x + 2) = 5

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

= 5 (x^{3} + 4 x) + (3 x^{2} + 4) (5 x + 2)

Vereinfache

5 (x^{3} + 4 x) + (3 x^{2} + 4) (5 x + 2) : 20 x^{3} + 6 x^{2} + 40 x + 8

= 20 x^{3} + 6 x^{2} + 40 x + 8

d er i v a t i v e 12 x^{2} - 24 x

\int 9 - r^{2} r d r

\int \frac{( a - b ) ^{4}}{a x} d x

\frac{d y}{d x} = 4 y x

t an g e n t f (x) = 8 x^{2} + 4, at x = - 7