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Beliebt Rechnen >

(dy)/(dx)= 1/(sqrt(1-x^2))-1/(sqrt(x))

Lösung

\frac{d y}{d x} = \frac{1}{1 - x ^{2}} - \frac{1}{x}

Lösung

y = arcsin (x) - 2 x + c_{1}

Schritte zur Lösung

\frac{d y}{d x} = \frac{1}{1 - x ^{2}} - \frac{1}{x}

Ersetze

\frac{d y}{d x}

mit

y^{'} (x)

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

Wenn

f^{^{'}} (x) = g (x)

dann

f (x) = \int g (x) d x

y = \int \frac{1}{1 - x ^{2}} - \frac{1}{x} d x

\int \frac{1}{1 - x ^{2}} - \frac{1}{x} d x = arcsin (x) - 2 x + c_{1}

y = arcsin (x) - 2 x + c_{1}

Graph

Beliebte Beispiele

derivative x^2+4x+6

d er i v a t i v e x^{2} + 4 x + 6

integral of x^2ln(x^2)

\int x^{2} ln (x^{2}) d x

laplacetransform 2t^2-t+1

l a pl a ce t r an s f or m 2 t^{2} - t + 1

integral of (5x+4)^2

\int (5 x + 4)^{2} d x

integral of x^3sqrt(9-x^2)

\int x^{3} 9 - x^{2} d x