derivative f(x)= 1/4 x^8-1/2 x^6-x+2

Lösung

ableitung von

f (x) = \frac{1}{4} x^{8} - \frac{1}{2} x^{6} - x + 2

2 x^{7} - 3 x^{5} - 1

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{4} x^{8} - \frac{1}{2} x^{6} - x + 2)

Vereinfache

\frac{1}{4} x^{8} - \frac{1}{2} x^{6} - x + 2 : \frac{x ^{8}}{4} - \frac{x ^{6}}{2} - x + 2

= \frac{d}{d x} (\frac{x ^{8}}{4} - \frac{x ^{6}}{2} - x + 2)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{x ^{8}}{4}) - \frac{d}{d x} (\frac{x ^{6}}{2}) - \frac{d x}{d x} + \frac{d}{d x} (2)

\frac{d}{d x} (\frac{x ^{8}}{4}) = 2 x^{7}

\frac{d}{d x} (\frac{x ^{6}}{2}) = 3 x^{5}

\frac{d x}{d x} = 1

\frac{d}{d x} (2) = 0

= 2 x^{7} - 3 x^{5} - 1 + 0

Vereinfache

= 2 x^{7} - 3 x^{5} - 1

d er i v a t i v e y = \frac{4}{x}

s l o p e x = 6

d er i v a t i v e f (x) = 4 e^{x} cos (x)

d er i v a t i v e f (x) = x^{2} - 4 x

c a r t es ian (- 3, \frac{5 π}{6})