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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

Graph

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