derivative of (x^3-2x+1(3x^3+2x^2-5x))

Lösung

\frac{d}{d x} ((x^{3} - 2 x + 1) (3 x^{3} + 2 x^{2} - 5 x))

18 x^{5} + 10 x^{4} - 44 x^{3} - 3 x^{2} + 24 x - 5

Schritte zur Lösung

\frac{d}{d x} ((x^{3} - 2 x + 1) (3 x^{3} + 2 x^{2} - 5 x))

Wende die Produktregel an:

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

f = x^{3} - 2 x + 1, g = 3 x^{3} + 2 x^{2} - 5 x

= \frac{d}{d x} (x^{3} - 2 x + 1) (3 x^{3} + 2 x^{2} - 5 x) + \frac{d}{d x} (3 x^{3} + 2 x^{2} - 5 x) (x^{3} - 2 x + 1)

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

\frac{d}{d x} (3 x^{3} + 2 x^{2} - 5 x) = 9 x^{2} + 4 x - 5

= (3 x^{2} - 2) (3 x^{3} + 2 x^{2} - 5 x) + (9 x^{2} + 4 x - 5) (x^{3} - 2 x + 1)

Vereinfache

(3 x^{2} - 2) (3 x^{3} + 2 x^{2} - 5 x) + (9 x^{2} + 4 x - 5) (x^{3} - 2 x + 1) : 18 x^{5} + 10 x^{4} - 44 x^{3} - 3 x^{2} + 24 x - 5

= 18 x^{5} + 10 x^{4} - 44 x^{3} - 3 x^{2} + 24 x - 5

x \to - \infty lim (\frac{x}{- 1})

\frac{\partial}{\partial y} (e^{y x} y^{2})

d er i v a t i v e f (x) = (x - 4) (x^{2} + 8)

y^{^{'}} = 4 y + y^{4}

\frac{d}{d x} (\frac{x ^{2} - 9 x + 14}{( x - 5 ) ( x - 10 )})