derivative f(x)=9-|x-4|\at x

Lösung

ableitung von

f (x) = 9 - ∣ x - 4 ∣ at x

- \frac{2 x ^{2} - 12 x + 16}{∣ x - 4 ∣}

Schritte zur Lösung

\frac{d}{d x} (9 - ∣ x - 4 ∣ x)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (9) - \frac{d}{d x} (∣ x - 4 ∣ x)

\frac{d}{d x} (9) = 0

\frac{d}{d x} (∣ x - 4 ∣ x) = \frac{2 x ^{2} - 12 x + 16}{∣ x - 4 ∣}

= 0 - \frac{2 x ^{2} - 12 x + 16}{∣ x - 4 ∣}

Vereinfache

= - \frac{2 x ^{2} - 12 x + 16}{∣ x - 4 ∣}

x \to 5 - lim (\frac{2}{x ^{2} - 25})

\int \frac{10}{( x + 1 ) ( x ^{2} + 9 )} d x

s im pl i f y (e^{- x} - e^{2}) (e^{x} + e^{- 5})

s l o p e (2, 0), (32, - 5)

\int 27 sec^{4} (x) d x