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Beliebt Rechnen >

(dy)/(dx)= x/(4+x^2)

Lösung

\frac{d y}{d x} = \frac{x}{4 + x ^{2}}

Lösung

y = \frac{1}{2} ln (4 + x^{2}) + c_{1}

Schritte zur Lösung

\frac{d y}{d x} = \frac{x}{4 + x ^{2}}

Ersetze

\frac{d y}{d x}

mit

y^{'} (x)

y^{^{'}} (x) = \frac{x}{4 + x ^{2}}

Wenn

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

dann

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

y = \int \frac{x}{4 + x ^{2}} d x

\int \frac{x}{4 + x ^{2}} d x = \frac{1}{2} ln (4 + x^{2}) + c_{1}

y = \frac{1}{2} ln (4 + x^{2}) + c_{1}

Graph

Beliebte Beispiele

derivative of 2^xln(x)

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

integral of (x^2)/(sqrt(x^3+1))

\int \frac{x ^{2}}{x ^{3} + 1} d x

f (x) = e^{x^{2} + 1}

derivative f(x)=10^{sqrt(x)}

d er i v a t i v e f (x) = 1 0^{x}

derivative of (2x/(x^2+4))

\frac{d}{d x} (\frac{2 x}{x ^{2} + 4})