derivative y=xarcsin(x)+sqrt(1-x^2)

Lösung

ableitung von

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

arcsin (x)

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Vereinfache

= arcsin (x)

\int \frac{x ^{2}}{x ^{6} + 9} d x

\int \frac{4 x}{( x ^{2} + 1 ) ( x ^{2} + 2 x + 3 )} d x

\int_{0}^{10} 20 t e^{- 0.6 t} d t

\frac{d}{d x} (arccos (\frac{x}{2}))

y^{^{'}} = \frac{( x ^{2} + 3 y ^{2} )}{2 x y}