derivative of arcsin(1/2 x)

Lösung

\frac{d}{d x} (arcsin (\frac{1}{2} x))

\frac{1}{4 - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (arcsin (\frac{1}{2} x))

Vereinfache

arcsin (\frac{1}{2} x) : arcsin (\frac{x}{2})

= \frac{d}{d x} (arcsin (\frac{x}{2}))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= \frac{1}{4 - x ^{2}}

\frac{\partial}{\partial x} (arctan (\frac{x}{3}))

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

x \to 2 lim (\frac{x ^{3} - 8}{2 x})

\frac{\partial}{\partial x} (x e^{x y} - 2 y + 1)

x \to 3 lim (cos (\frac{1}{x - 3}))