derivative of sin(x+arcsin(x))

Lösung

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

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (sin (x)) + \frac{d}{d x} (arcsin (x))

\frac{d}{d x} (sin (x)) = cos (x)

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

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