derivative of sqrt(4x^2-8x)

Lösung

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

\frac{2 ( x - 1 )}{x ( x - 2 )}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{2 4 x ^{2} - 8 x} (8 x - 8) : \frac{2 ( x - 1 )}{x ( x - 2 )}

= \frac{2 ( x - 1 )}{x ( x - 2 )}

x \to 16 lim (\frac{x - 4}{4 x - 2})

x \to \infty lim (e^{- 3 x} sin (x))

d er i v a t i v e - 4 sin (x) - 9 ln (x) + 11

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

\int \frac{30}{( x - 1 ) ( x ^{2} + 9 )} d x