derivative of (arcsin(x)/x)

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d x}{d x} = 1

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

Vereinfache

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

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

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

\int \frac{- 5 x}{( x ^{2} + 5 ) ^{\frac{3}{2}}} d x

d er i v a t i v e y = x ln (sin^{2} (x))

y (x + 7) + \frac{d y}{d x} = 0

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