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Beliebt Rechnen >

(\partial)/(\partial x)(xy+xe^{1/y})

Lösung

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

Lösung

y + e^{\frac{1}{y}}

Schritte zur Lösung

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

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} (x e^{\frac{1}{y}})

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

\frac{\partial}{\partial x} (x e^{\frac{1}{y}}) = e^{\frac{1}{y}}

= y + e^{\frac{1}{y}}

Beliebte Beispiele

integral of sec^2(u)

\int sec^{2} (u) d u

integral of (32)/(x^2-64)

\int \frac{32}{x ^{2} - 64} d x

integral of ((ln(u))^4)/u

\int \frac{( ln ( u ) ) ^{4}}{u} d u

integral of x^3cos(12x)

\int x^{3} cos (12 x) d x

limit as x approaches 0 of (x-1)/(x^2+1)

x \to 0 lim (\frac{x - 1}{x ^{2} + 1})