(\partial)/(\partial x)(xarcsin(x)y)

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

= y \frac{\partial}{\partial x} (x arcsin (x))

Wende die Produktregel an:

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

f = x, g = arcsin (x)

= y (\frac{\partial}{\partial x} (x) arcsin (x) + \frac{\partial}{\partial x} (arcsin (x)) x)

\frac{\partial}{\partial x} (x) = 1

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

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

Vereinfache

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

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

\int_{0}^{\frac{π}{2}} x sin (4 x) d x

t a y l or 4 x

\int 3 + s (s + 1)^{2} d s

d er i v a t i v e f (x) = ln (25 sin^{2} (x))

d er i v a t i v e y (X) = 0.167 X