derivative y=6-5x^9+2x^8-2x^6

Lösung

ableitung von

y = 6 - 5 x^{9} + 2 x^{8} - 2 x^{6}

- 45 x^{8} + 16 x^{7} - 12 x^{5}

Schritte zur Lösung

\frac{d}{d x} (6 - 5 x^{9} + 2 x^{8} - 2 x^{6})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (6) - \frac{d}{d x} (5 x^{9}) + \frac{d}{d x} (2 x^{8}) - \frac{d}{d x} (2 x^{6})

\frac{d}{d x} (6) = 0

\frac{d}{d x} (5 x^{9}) = 45 x^{8}

\frac{d}{d x} (2 x^{8}) = 16 x^{7}

\frac{d}{d x} (2 x^{6}) = 12 x^{5}

= 0 - 45 x^{8} + 16 x^{7} - 12 x^{5}

Vereinfache

= - 45 x^{8} + 16 x^{7} - 12 x^{5}

t an g e n t f (x) = \frac{2 x}{3 x - 1}, at x = 1

s l o p e y = - 4

mi d p o in t (- 2, 3), (10, 3)

d er i v a t i v e x^{2} - 3 x + 4

d er i v a t i v e f (x) = \frac{x}{x ^{2} + 1}