derivative (2-x-3x^3)(7+x^5)

Lösung

ableitung von

(2 - x - 3 x^{3}) (7 + x^{5})

- 24 x^{7} - 6 x^{5} + 10 x^{4} - 63 x^{2} - 7

Schritte zur Lösung

\frac{d}{d x} ((2 - x - 3 x^{3}) (7 + x^{5}))

Wende die Produktregel an:

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

f = 2 - x - 3 x^{3}, g = 7 + x^{5}

= \frac{d}{d x} (2 - x - 3 x^{3}) (7 + x^{5}) + \frac{d}{d x} (7 + x^{5}) (2 - x - 3 x^{3})

\frac{d}{d x} (2 - x - 3 x^{3}) = - 9 x^{2} - 1

\frac{d}{d x} (7 + x^{5}) = 5 x^{4}

= (- 9 x^{2} - 1) (7 + x^{5}) + 5 x^{4} (2 - x - 3 x^{3})

Vereinfache

(- 9 x^{2} - 1) (7 + x^{5}) + 5 x^{4} (2 - x - 3 x^{3}) : - 24 x^{7} - 6 x^{5} + 10 x^{4} - 63 x^{2} - 7

= - 24 x^{7} - 6 x^{5} + 10 x^{4} - 63 x^{2} - 7