derivative f(x)=(2x^3+5x)(x-3)(x+2)

Lösung

ableitung von

f (x) = (2 x^{3} + 5 x) (x - 3) (x + 2)

10 x^{4} - 8 x^{3} - 21 x^{2} - 10 x - 30

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d}{d x} (2 x^{3} + 5 x) = 6 x^{2} + 5

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

= (6 x^{2} + 5) (x - 3) (x + 2) + (2 x - 1) (2 x^{3} + 5 x)

Vereinfache

(6 x^{2} + 5) (x - 3) (x + 2) + (2 x - 1) (2 x^{3} + 5 x) : 10 x^{4} - 8 x^{3} - 21 x^{2} - 10 x - 30

= 10 x^{4} - 8 x^{3} - 21 x^{2} - 10 x - 30

x \to π lim (3 cot (x))

\int \frac{15 e ^{5 r}}{e ^{5 r} + 2} d r

t an g e n t y = - 3 cos (x), at x = \frac{3 π}{4}

\int (x + 1)^{3} d x

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