derivative of 2xarcsin(x)

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

= 2 \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)

= 2 (\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}}

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

Vereinfache

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

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

x \to 2 lim ([x])

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

\frac{d}{d x} (x^{2} lo g_{e} (2 x))

\frac{d y}{d x} + 4 tan (4 x) y = 3 cos (4 x)

s l o p e (0, 1), (4, - 5)