derivative f(x)=x(x-1)(x-2)

Lösung

ableitung von

f (x) = x (x - 1) (x - 2)

3 x^{2} - 6 x + 2

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = (x - 1) (x - 2)

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

\frac{d x}{d x} = 1

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

= 1 \cdot (x - 1) (x - 2) + (2 x - 3) x

Vereinfache

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

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

f (x) = 5^{c o s (2 \frac{π}{2})}

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

x \to - \infty lim (- \frac{1}{0})

n = 0 \sum \infty 3 - (0.5)^{n}

\int_{1}^{\infty} \frac{1}{x ^{6}} d x