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

Lösung

ableitung von

(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

\frac{d}{d x} (ln (y - x))

- x^{2} + 8 x - 9, (\frac{1}{2} x) + 1, x = 3, x = 5

\int_{- \infty}^{0} \frac{1}{7 - 5 x} d x

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

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