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

Lösung

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

3 x^{2} - 8 x + 5

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

2 (x - 1) (x - 2) + 1 \cdot (x - 1)^{2} : 3 x^{2} - 8 x + 5

= 3 x^{2} - 8 x + 5

d er i v a t i v e f (x) = sin (x^{3})

\frac{\partial}{\partial x} (Q (x) 0. 5^{\frac{x}{35}})

n = 0 \sum \infty \frac{n}{n ^{2} + 1}

d er i v a t i v e f (x) = (3 x^{2} + 4 x + 1)^{10}

d er i v a t i v e f (x) = 6 x^{2} + 3 x - 4