derivative f(x)=1100(sqrt(x^2-0.2x))

Lösung

ableitung von

f (x) = 1100 (x^{2} - 0.2 x)

\frac{550 ( 2 x - 0.2 )}{x ^{2} - 0.2 x}

Schritte zur Lösung

\frac{d}{d x} (1100 x^{2} - 0.2 x)

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 1100 \frac{d}{d x} (x^{2} - 0.2 x)

Wende die Kettenregel an:

\frac{1}{2 x ^{2} - 0.2 x} \frac{d}{d x} (x^{2} - 0.2 x)

= \frac{1}{2 x ^{2} - 0.2 x} \frac{d}{d x} (x^{2} - 0.2 x)

\frac{d}{d x} (x^{2} - 0.2 x) = 2 x - 0.2

= 1100 \cdot \frac{1}{2 x ^{2} - 0.2 x} (2 x - 0.2)

Vereinfache

1100 \cdot \frac{1}{2 x ^{2} - 0.2 x} (2 x - 0.2) : \frac{550 ( 2 x - 0.2 )}{x ^{2} - 0.2 x}

= \frac{550 ( 2 x - 0.2 )}{x ^{2} - 0.2 x}

t an g e n t y = - 2 sin (x), at x = \frac{3}{4} π

n = 0 \sum \infty \frac{4 n}{- 4 n + 7}

d er i v a t i v e f (x) = 30 + 10 e^{- 0.05 x}

x \to 0 lim (\frac{f ( x )}{x})

x \to - 2 lim (x (x - 1))