derivative f(x)=(x-2)^2(x+3)^3

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

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