derivative of (x^3-4x^2-6x+1(x^2-3x+1))

Lösung

\frac{d}{d x} ((x^{3} - 4 x^{2} - 6 x + 1) (x^{2} - 3 x + 1))

5 x^{4} - 28 x^{3} + 21 x^{2} + 30 x - 9

Schritte zur Lösung

\frac{d}{d x} ((x^{3} - 4 x^{2} - 6 x + 1) (x^{2} - 3 x + 1))

Wende die Produktregel an:

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

f = x^{3} - 4 x^{2} - 6 x + 1, g = x^{2} - 3 x + 1

= \frac{d}{d x} (x^{3} - 4 x^{2} - 6 x + 1) (x^{2} - 3 x + 1) + \frac{d}{d x} (x^{2} - 3 x + 1) (x^{3} - 4 x^{2} - 6 x + 1)

\frac{d}{d x} (x^{3} - 4 x^{2} - 6 x + 1) = 3 x^{2} - 8 x - 6

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

= (3 x^{2} - 8 x - 6) (x^{2} - 3 x + 1) + (2 x - 3) (x^{3} - 4 x^{2} - 6 x + 1)

Vereinfache

(3 x^{2} - 8 x - 6) (x^{2} - 3 x + 1) + (2 x - 3) (x^{3} - 4 x^{2} - 6 x + 1) : 5 x^{4} - 28 x^{3} + 21 x^{2} + 30 x - 9

= 5 x^{4} - 28 x^{3} + 21 x^{2} + 30 x - 9

l a pl a ce t r an s f or m 13 e^{4 t} e^{2}

d er i v a t i v e - 10 ln (x e^{x^{8}})

\int 6 y (x - y) d y

x \to 0 lim (\frac{2 x + 4 - 2}{x + 1 - 1})

\frac{\partial}{\partial x} (x yz x)