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Beliebt Rechnen >

d/(dy)(x+1/2 ln(x^2+y^2))

Lösung

\frac{d}{d y} (x + \frac{1}{2} ln (x^{2} + y^{2}))

Lösung

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

Schritte zur Lösung

\frac{d}{d y} (x + \frac{1}{2} ln (x^{2} + y^{2}))

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d x}{d y} = 0

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

= 0 + \frac{y}{x ^{2} + y ^{2}}

Vereinfache

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

Beliebte Beispiele

integral of 5tan^2(x)+tan^4(x)

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

integral of e^{(-x^2)}

\int e^{(- x^{2})} d x

fläche y=x^2,y=2-x,x=0

a re a y = x^{2}, y = 2 - x, x = 0

derivative f(x)=ln((e^x)/(1+e^x))

d er i v a t i v e f (x) = ln (\frac{e ^{x}}{1 + e ^{x}})

derivative y=ln(3/x)

d er i v a t i v e y = ln (\frac{3}{x})