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

Lösung

ableitung von

(x - 2)^{2} (x - 1)

3 x^{2} - 10 x + 8

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

2 (x - 2) (x - 1) + 1 \cdot (x - 2)^{2} : 3 x^{2} - 10 x + 8

= 3 x^{2} - 10 x + 8

\frac{d v}{d t} = 0.64 - \frac{v}{29400} \cdot 8, v (0) = 0

l a pl a ce t r an s f or m cos (2 (t + 1))

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

\frac{\partial}{\partial x} (x^{y} ln (x))

\frac{\partial}{\partial L} (L^{\frac{1}{2}} K^{\frac{1}{2}})