derivative of 5xarcsin(x)

Lösung

\frac{d}{d x} (5 x arcsin (x))

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

Schritte zur Lösung

\frac{d}{d x} (5 x arcsin (x))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} (x arcsin (x))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = arcsin (x)

= 5 (\frac{d x}{d x} arcsin (x) + \frac{d}{d x} (arcsin (x)) x)

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

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

= 5 (1 \cdot arcsin (x) + \frac{1}{1 - x ^{2}} x)

Vereinfache

5 (1 \cdot arcsin (x) + \frac{1}{1 - x ^{2}} x) : 5 (arcsin (x) + \frac{x}{1 - x ^{2}})

= 5 (arcsin (x) + \frac{x}{1 - x ^{2}})