derivative of x^2(x-1^3)

Lösung

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

2 x (x - 1)^{3} + 3 (x - 1)^{2} x^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{2}, g = (x - 1)^{3}

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

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

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

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

x \to 0 lim (\frac{( 2. 8 ^{x} - 1 )}{x})

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