derivative of (x^2+3x(x-2)(x^2+1))

Lösung

\frac{d}{d x} ((x^{2} + 3 x) (x - 2) (x^{2} + 1))

5 x^{4} + 4 x^{3} - 15 x^{2} + 2 x - 6

Schritte zur Lösung

\frac{d}{d x} ((x^{2} + 3 x) (x - 2) (x^{2} + 1))

Wende die Produktregel an:

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

f = x^{2} + 3 x, g = (x - 2) (x^{2} + 1)

= \frac{d}{d x} (x^{2} + 3 x) (x - 2) (x^{2} + 1) + \frac{d}{d x} ((x - 2) (x^{2} + 1)) (x^{2} + 3 x)

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

\frac{d}{d x} ((x - 2) (x^{2} + 1)) = 3 x^{2} - 4 x + 1

= (2 x + 3) (x - 2) (x^{2} + 1) + (3 x^{2} - 4 x + 1) (x^{2} + 3 x)

Vereinfache

(2 x + 3) (x - 2) (x^{2} + 1) + (3 x^{2} - 4 x + 1) (x^{2} + 3 x) : 5 x^{4} + 4 x^{3} - 15 x^{2} + 2 x - 6

= 5 x^{4} + 4 x^{3} - 15 x^{2} + 2 x - 6

a re a y = 2 x - x^{2}, (0, 2)

d er i v a t i v e 9 sin (3 x)

\int_{0}^{1} - x + 2 d x

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

in v erse l a pl a ce \frac{- 40 x - 80}{x ^{2} + 3 x + 1}