derivative 3xarcsin(x)

Lösung

ableitung von

3 x arcsin (x)

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

Schritte zur Lösung

\frac{d}{d x} (3 x arcsin (x))

Entferne die Konstante:

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

= 3 \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)

= 3 (\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}}

= 3 (1 \cdot arcsin (x) + \frac{1}{1 - x ^{2}} x)

Vereinfache

3 (1 \cdot arcsin (x) + \frac{1}{1 - x ^{2}} x) : 3 (arcsin (x) + \frac{x}{1 - x ^{2}})

= 3 (arcsin (x) + \frac{x}{1 - x ^{2}})

\frac{d}{d x} (\frac{2 ( 3 x ^{4} - 5 )}{x ^{3}})

s l o p e in t erce pt (- 2.2) (0)

a re a y = 6 x^{2}, y = x^{2} + 4

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

\frac{\partial}{\partial y} (arctan (x))