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

Lösung

ableitung von

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

- 12 x^{5} + 5 x^{4} - 8 x^{3} - 3 x^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d}{d x} (- 2 x^{3} + x^{2} - 2 x - 1) = - 6 x^{2} + 2 x - 2

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

= (- 6 x^{2} + 2 x - 2) x^{3} + 3 x^{2} (- 2 x^{3} + x^{2} - 2 x - 1)

Vereinfache

(- 6 x^{2} + 2 x - 2) x^{3} + 3 x^{2} (- 2 x^{3} + x^{2} - 2 x - 1) : - 12 x^{5} + 5 x^{4} - 8 x^{3} - 3 x^{2}

= - 12 x^{5} + 5 x^{4} - 8 x^{3} - 3 x^{2}

\frac{d}{d x} (2 e^{5 x})

\int 2 x y + 2 x d x

f (t) = sin^{2} (t)

x \to 3 lim (\frac{x ^{2} + x}{x + 3})

\int \frac{13}{x ^{2} - 1} d x