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

Lösung

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

- 4 x^{3} + 9 x^{2} - 6

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d}{d x} (x - 1) = 1

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

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

Vereinfache

1 \cdot (x - 2) (2 - x^{2}) + (2 - 3 x^{2} + 4 x) (x - 1) : - 4 x^{3} + 9 x^{2} - 6

= - 4 x^{3} + 9 x^{2} - 6

d er i v a t i v e \frac{3}{6 t + 3}

f^{^{'}} (t) = \frac{8 t}{8 + t}

y^{^{''}} + 8 y^{^{'}} + 65 y = 0, y (0) = 0, y^{^{'}} (0) = 0

x \to - 2 lim (x^{2} - 2 x^{2} + 2 x + 3)

\int \frac{8}{x ^{2} - 1} d x