derivative of arcsin((ax/4))

Lösung

\frac{d}{d x} (arcsin (\frac{a x}{4}))

\frac{a}{16 - a ^{2} x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (arcsin (\frac{a x}{4}))

Wende die Kettenregel an:

\frac{1}{1 - ( \frac{a x}{4} ) ^{2}} \frac{d}{d x} (\frac{a x}{4})

= \frac{1}{1 - ( \frac{a x}{4} ) ^{2}} \frac{d}{d x} (\frac{a x}{4})

\frac{d}{d x} (\frac{a x}{4}) = \frac{a}{4}

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

Vereinfache

\frac{1}{1 - ( \frac{a x}{4} ) ^{2}} \cdot \frac{a}{4} : \frac{a}{16 - a ^{2} x ^{2}}

= \frac{a}{16 - a ^{2} x ^{2}}

\frac{\partial}{\partial y} (- 5 e^{x} cos (yz))

\int \frac{a}{2} x + \frac{a}{2} d x

x \to 8 lim (2 x - 7 x^{2})

\frac{d}{d x} (\frac{x + y}{x - y})

t an g e n t f (x) = x^{4} - 18 x^{2} + 81, at x = 1