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

Lösung

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

- 6 x^{5} + 2 x - 2

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

= - 6 x^{5} + 2 x - 2

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

\frac{d}{d x} (40320 x)

\int_{- 6}^{- 10} \frac{1}{x + 2} d x

t an g e n t f (x) = x^{2} - 5, (3, 4)

d er i v a t i v e y = \frac{1}{x ^{7}}