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

Lösung

ableitung von

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

- 8 x^{3} + 6 x^{2} - 2 x + 1

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d}{d x} (1 + 2 x^{2}) = 4 x

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

= 4 x (x - x^{2}) + (1 - 2 x) (1 + 2 x^{2})

Vereinfache

4 x (x - x^{2}) + (1 - 2 x) (1 + 2 x^{2}) : - 8 x^{3} + 6 x^{2} - 2 x + 1

= - 8 x^{3} + 6 x^{2} - 2 x + 1

d er i v a t i v e (x^{3} + 8 x)^{3}

\int_{0}^{\frac{π}{2}} π sin^{2} (x) d x

\frac{d}{d x} (7 + 7 x)

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\frac{d}{d x} (\frac{4 x ^{3}}{3} + 2 x + cos (x) + 1)