derivative of (arcsin(x)/(sqrt(1-x^2)))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

x \to 8 - lim (\frac{64 - x ^{2}}{x - 8})

\frac{d}{d x} (x 64 - x^{2})

\frac{d}{d x} (3 \frac{3 x}{x + 2})

d er i v a t i v e f (t) = \frac{3 t}{t - 3}

\int_{0}^{5} π (25 - x^{2}) d x