derivative of arcsin(x/3)

Lösung

\frac{d}{d x} (arcsin (\frac{x}{3}))

\frac{1}{9 - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (arcsin (\frac{x}{3}))

Wende die Kettenregel an:

\frac{1}{1 - ( \frac{x}{3} ) ^{2}} \frac{d}{d x} (\frac{x}{3})

= \frac{1}{1 - ( \frac{x}{3} ) ^{2}} \frac{d}{d x} (\frac{x}{3})

\frac{d}{d x} (\frac{x}{3}) = \frac{1}{3}

= \frac{1}{1 - ( \frac{x}{3} ) ^{2}} \cdot \frac{1}{3}

Vereinfache

\frac{1}{1 - ( \frac{x}{3} ) ^{2}} \cdot \frac{1}{3} : \frac{1}{9 - x ^{2}}

= \frac{1}{9 - x ^{2}}

\int \frac{4 x + 1}{4 x} d x

n = 1 \sum \infty \frac{1}{n ^{2}} - \frac{1}{n}

x \to 5 lim (x^{2} - 25)

\int \frac{2}{( x ^{2} - 3 x + 2 )} d x

d er i v a t i v e f (t) = \frac{t}{t ^{2} + 7}