derivative x^2(1-8x)

Lösung

ableitung von

x^{2} (1 - 8 x)

2 x - 24 x^{2}

Schritte zur Lösung

\frac{d}{d x} (x^{2} (1 - 8 x))

Wende die Produktregel an:

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

f = x^{2}, g = 1 - 8 x

= \frac{d}{d x} (x^{2}) (1 - 8 x) + \frac{d}{d x} (1 - 8 x) x^{2}

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

\frac{d}{d x} (1 - 8 x) = - 8

= 2 x (1 - 8 x) + (- 8) x^{2}

Vereinfache

2 x (1 - 8 x) + (- 8) x^{2} : 2 x - 24 x^{2}

= 2 x - 24 x^{2}

t \to 0 lim (tan (7 t))

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