derivative of (x^3-3x(2x^2+3x+5))

Lösung

\frac{d}{d x} ((x^{3} - 3 x) (2 x^{2} + 3 x + 5))

10 x^{4} + 12 x^{3} - 3 x^{2} - 18 x - 15

Schritte zur Lösung

\frac{d}{d x} ((x^{3} - 3 x) (2 x^{2} + 3 x + 5))

Wende die Produktregel an:

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

f = x^{3} - 3 x, g = 2 x^{2} + 3 x + 5

= \frac{d}{d x} (x^{3} - 3 x) (2 x^{2} + 3 x + 5) + \frac{d}{d x} (2 x^{2} + 3 x + 5) (x^{3} - 3 x)

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

\frac{d}{d x} (2 x^{2} + 3 x + 5) = 4 x + 3

= (3 x^{2} - 3) (2 x^{2} + 3 x + 5) + (4 x + 3) (x^{3} - 3 x)

Vereinfache

(3 x^{2} - 3) (2 x^{2} + 3 x + 5) + (4 x + 3) (x^{3} - 3 x) : 10 x^{4} + 12 x^{3} - 3 x^{2} - 18 x - 15

= 10 x^{4} + 12 x^{3} - 3 x^{2} - 18 x - 15

n = 0 \sum \infty \frac{1}{3 ^{n}}

f (x) = 7 ln (x)

\int \frac{15}{25 + x ^{2}} d x

x \to - 2 lim (\frac{2}{x + 2})

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