derivative arcsin(x/2)

Lösung

ableitung von

arcsin (\frac{x}{2})

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

Schritte zur Lösung

\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{d y}{d x} = \frac{2 x}{x + 2}

\int \frac{12}{x ^{5}} d x

n \to \infty lim (e^{3 n^{2}})

\frac{\partial}{\partial y} (17 - x^{2} - 4 y^{2})

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