derivative f(x)=6xarcsin(x)

Lösung

ableitung von

f (x) = 6 x arcsin (x)

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

Schritte zur Lösung

\frac{d}{d x} (6 x arcsin (x))

Entferne die Konstante:

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

= 6 \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)

= 6 (\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}}

= 6 (1 \cdot arcsin (x) + \frac{1}{1 - x ^{2}} x)

Vereinfache

6 (1 \cdot arcsin (x) + \frac{1}{1 - x ^{2}} x) : 6 (arcsin (x) + \frac{x}{1 - x ^{2}})

= 6 (arcsin (x) + \frac{x}{1 - x ^{2}})

\frac{\partial}{\partial x} (arcsin (4 x yz))

t an g e n t f (x) = 18 x + 18, (1, 6)

(2 x y + 2 y^{2}) d x + (x^{2} + 4 x y) d y = 0

d er i v a t i v e x^{3} (x - 2)^{2}

\int 27 x^{2} d x