derivative f(x)= 1/9 x^3+1/21 x-19

Lösung

ableitung von

f (x) = \frac{1}{9} x^{3} + \frac{1}{21} x - 19

\frac{x ^{2}}{3} + \frac{1}{21}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{9} x^{3} + \frac{1}{21} x - 19)

Vereinfache

\frac{1}{9} x^{3} + \frac{1}{21} x - 19 : \frac{x ^{3}}{9} + \frac{x}{21} - 19

= \frac{d}{d x} (\frac{x ^{3}}{9} + \frac{x}{21} - 19)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{x ^{3}}{9}) + \frac{d}{d x} (\frac{x}{21}) - \frac{d}{d x} (19)

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

\frac{d}{d x} (\frac{x}{21}) = \frac{1}{21}

\frac{d}{d x} (19) = 0

= \frac{x ^{2}}{3} + \frac{1}{21} - 0

Vereinfache

= \frac{x ^{2}}{3} + \frac{1}{21}

d er i v a t i v e f (x) = x + 3

t an g e n t f (x) = x, at x = 9

d er i v a t i v e x^{2} - 4 x + 5

d er i v a t i v e y = 2 x + 5

d er i v a t i v e x (x - 4)^{3}