derivative f(x)=x^4(3-x)^3

Lösung

ableitung von

f (x) = x^{4} (3 - x)^{3}

4 x^{3} (3 - x)^{3} - 3 x^{4} (3 - x)^{2}

Schritte zur Lösung

\frac{d}{d x} (x^{4} (3 - x)^{3})

Wende die Produktregel an:

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

f = x^{4}, g = (3 - x)^{3}

= \frac{d}{d x} (x^{4}) (3 - x)^{3} + \frac{d}{d x} ((3 - x)^{3}) x^{4}

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

= 4 x^{3} (3 - x)^{3} + (- 3 (3 - x)^{2}) x^{4}

Vereinfache

= 4 x^{3} (3 - x)^{3} - 3 x^{4} (3 - x)^{2}

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