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

Lösung

\frac{d}{d x} ((- 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{\partial}{\partial v} (u (v) (v)^{2} e^{v})

\frac{d}{d x} (\frac{d y}{d x}) = 0

d er i v a t i v e \frac{6 x ^{2} + 8 x + 2}{x}

\frac{\partial}{\partial x} (ln (\frac{y ^{9}}{x ^{7}}))

x \to 0 lim (+ (\frac{ln ( x )}{x}))