derivative f(x)=x^3(2x-1)

Lösung

ableitung von

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

8 x^{3} - 3 x^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

3 x^{2} (2 x - 1) + 2 x^{3} : 8 x^{3} - 3 x^{2}

= 8 x^{3} - 3 x^{2}

x \to 0 + lim (\frac{sin ( x )}{x ^{\frac{1}{2}}})

\int_{- \infty}^{0} x^{2} e^{- x} d x

\frac{d}{d x} ((1 - x) e^{x})

a re a 2 y = 3 x, 2 y + 3 x = 6, y = 4

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