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Beliebt Rechnen >

(\partial)/(\partial y)(xy+1/x+1/y)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

\frac{\partial}{\partial y} (\frac{1}{x}) = 0

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

= x + 0 - \frac{1}{y ^{2}}

Vereinfache

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

Beliebte Beispiele

integral of tan^3(10x)

\int tan^{3} (10 x) d x

integral of (5x-3)/(x^2-2x-3)

\int \frac{5 x - 3}{x ^{2} - 2 x - 3} d x

(\partial)/(\partial x)((x+y)/(x-y))

\frac{\partial}{\partial x} (\frac{x + y}{x - y})

derivative of sin(cos(4x))

\frac{d}{d x} (sin (cos (4 x)))

derivative 1/(5x^{4/5)}

d er i v a t i v e \frac{1}{5 x ^{\frac{4}{5}}}