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Beliebt Rechnen >

(\partial}{\partial x}(xy+\frac{27)/x)

Lösung

\frac{\partial}{\partial x} (x y + \frac{27}{x})

Lösung

y - \frac{27}{x ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (x y + \frac{27}{x})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x y) + \frac{\partial}{\partial x} (\frac{27}{x})

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

\frac{\partial}{\partial x} (\frac{27}{x}) = - \frac{27}{x ^{2}}

= y - \frac{27}{x ^{2}}

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x \to \infty lim (\frac{2 x}{x})