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

Lösung

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

- 15 x^{4} + 15 x^{2} - 2

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

\frac{d}{d x} (- 3 x^{3} + 2 x) = - 9 x^{2} + 2

= 2 x (- 3 x^{3} + 2 x) + (- 9 x^{2} + 2) (x^{2} - 1)

Vereinfache

2 x (- 3 x^{3} + 2 x) + (- 9 x^{2} + 2) (x^{2} - 1) : - 15 x^{4} + 15 x^{2} - 2

= - 15 x^{4} + 15 x^{2} - 2

\frac{\partial}{\partial x} (2 x - 2 y)

x \to - 1 lim (h (x))

t an g e n t f (x) = \frac{8}{7 - x}

in v erse l a pl a ce {\frac{1}{s ^{2}} - \frac{48}{s ^{5}}}

\frac{d}{d θ} (3 cos (θ) - 4 sin (θ))