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Beliebt Rechnen >

(\partial)/(\partial x)(2xarcsin(x/y))

Lösung

\frac{\partial}{\partial x} (2 x arcsin (\frac{x}{y}))

Lösung

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

Schritte zur Lösung

\frac{\partial}{\partial x} (2 x arcsin (\frac{x}{y}))

Behandle

y

als Konstante

Entferne die Konstante:

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

= 2 \frac{\partial}{\partial x} (x arcsin (\frac{x}{y}))

Wende die Produktregel an:

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

f = x, g = arcsin (\frac{x}{y})

= 2 (\frac{\partial}{\partial x} (x) arcsin (\frac{x}{y}) + \frac{\partial}{\partial x} (arcsin (\frac{x}{y})) x)

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

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

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

Vereinfache

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

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

Beliebte Beispiele

fläche y=x^{-3},1<= x<= 5

a re a y = x^{- 3}, 1 \leq x \leq 5

derivative y=(-1)/(3sin^3(x))

d er i v a t i v e y = \frac{- 1}{3 sin ^{3} ( x )}

integral of (3t)

\int (3 t) d t

integral of x+tan(x)

\int x + tan (x) d x

limit as x approaches infinity of (3x^2+5x^3)/(2x^2-3x)

x \to \infty lim (\frac{3 x ^{2} + 5 x ^{3}}{2 x ^{2} - 3 x})