derivative (x-1)^2(x-1.05)^2

Lösung

ableitung von

(x - 1)^{2} (x - 1.05)^{2}

4 x^{3} - 12.3 x^{2} + 12.605 x - 4.305

Schritte zur Lösung

\frac{d}{d x} ((x - 1)^{2} (x - 1.05)^{2})

Wende die Produktregel an:

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

f = (x - 1)^{2}, g = (x - 1.05)^{2}

= \frac{d}{d x} ((x - 1)^{2}) (x - 1.05)^{2} + \frac{d}{d x} ((x - 1.05)^{2}) (x - 1)^{2}

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

\frac{d}{d x} ((x - 1.05)^{2}) = 2 (x - 1.05)

= 2 (x - 1) (x - 1.05)^{2} + 2 (x - 1.05) (x - 1)^{2}

Vereinfache

2 (x - 1) (x - 1.05)^{2} + 2 (x - 1.05) (x - 1)^{2} : 4 x^{3} - 12.3 x^{2} + 12.605 x - 4.305

= 4 x^{3} - 12.3 x^{2} + 12.605 x - 4.305

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