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Beliebt Rechnen >

(\partial)/(\partial x)(x/(x^2+y^2)+3x)

Lösung

\frac{\partial}{\partial x} (\frac{x}{x ^{2} + y ^{2}} + 3 x)

Lösung

\frac{- x ^{2} + y ^{2}}{( x ^{2} + y ^{2} ) ^{2}} + 3

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{x}{x ^{2} + y ^{2}} + 3 x)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (\frac{x}{x ^{2} + y ^{2}}) + \frac{\partial}{\partial x} (3 x)

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

\frac{\partial}{\partial x} (3 x) = 3

= \frac{- x ^{2} + y ^{2}}{( x ^{2} + y ^{2} ) ^{2}} + 3

Beliebte Beispiele

derivative of (2x/((x^2+1)))

limit as x approaches 5 of (6+1/x)^2

integral of (21)/(xln(8x))

fläche y^2-5x=1,x-y=1

implicit 9x^2+y^2=9