derivative y=arcsin(x/6)

Lösung

ableitung von

y = arcsin (\frac{x}{6})

\frac{1}{36 - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (arcsin (\frac{x}{6}))

Wende die Kettenregel an:

\frac{1}{1 - ( \frac{x}{6} ) ^{2}} \frac{d}{d x} (\frac{x}{6})

= \frac{1}{1 - ( \frac{x}{6} ) ^{2}} \frac{d}{d x} (\frac{x}{6})

\frac{d}{d x} (\frac{x}{6}) = \frac{1}{6}

= \frac{1}{1 - ( \frac{x}{6} ) ^{2}} \cdot \frac{1}{6}

Vereinfache

\frac{1}{1 - ( \frac{x}{6} ) ^{2}} \cdot \frac{1}{6} : \frac{1}{36 - x ^{2}}

= \frac{1}{36 - x ^{2}}

t an g e n t f (x) = x^{2} + 6

\int_{0}^{1} 36 π (x^{2} - x^{10}) d x

x \to 0 lim (1 - x)

\int \frac{9}{35 sin ( x ) - 12 cos ( x )} d x

\int (x + 1) (x^{2} + 2 x + 5)^{12} d x