derivative of (arcsin(3x)/x)

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (arcsin (3 x)) = \frac{3}{1 - 9 x ^{2}}

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

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

Vereinfache

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

= \frac{3 x - arcsin ( 3 x ) 1 - 9 x ^{2}}{x ^{2} 1 - 9 x ^{2}}

t an g e n t f (x) = 3 - 4 x^{2}, at x = - 2

t an g e n t y = 3 x, (3, 3)

\int e^{6 - 5 t} d t

\int x sin (3 t - 3 x) d x

\frac{\partial}{\partial y} (3 x + 2 y)