derivative of sqrt(2ax-x^2)

Lösung

\frac{d}{d x} (2 a x - x^{2})

\frac{a - x}{2 a x - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (2 a x - x^{2})

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= \frac{a - x}{2 a x - x ^{2}}

x \to 0 lim (\frac{cos ( 4 x ) - 1}{x})

x \to 0.1 lim (\frac{5 sin ( x )}{x})

x \to 6 lim (\frac{x ^{2} - 3 x - 18}{x - 6})

\int_{0}^{3} (x^{2} - 2 x) d x

x \to 3 lim (\frac{x ^{2} - 9}{x ^{2} - 10 x + 21})