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Beliebt Rechnen >

(\partial)/(\partial x)(y*arcsin(x/y))

Lösung

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

Lösung

\frac{y}{y ^{2} - x ^{2}}

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= \frac{y}{y ^{2} - x ^{2}}

Beliebte Beispiele

derivative sqrt(6t^2-t)

d er i v a t i v e 6 t^{2} - t

derivative f(x)=x^2tan(x)

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

integral of 1/(x^2+x-1)

\int \frac{1}{x ^{2} + x - 1} d x

integral from 1 to 4 of 4/(x^2+4x+4)

\int_{1}^{4} \frac{4}{x ^{2} + 4 x + 4} d x

limit as x approaches 0 of-2

x \to 0 lim (- 2)