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Beliebt Rechnen >

(\partial)/(\partial x)(4y+xe^{x/y})

Lösung

\frac{\partial}{\partial x} (4 y + x e^{\frac{x}{y}})

Lösung

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

Schritte zur Lösung

\frac{\partial}{\partial x} (4 y + x e^{\frac{x}{y}})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (4 y) + \frac{\partial}{\partial x} (x e^{\frac{x}{y}})

\frac{\partial}{\partial x} (4 y) = 0

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

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

Vereinfache

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

Beliebte Beispiele

integral of 7sec^2(x)

\int 7 sec^{2} (x) d x

integral of e^{5x}x

\int e^{5 x} x d x

integral of 2/(xsqrt(9x^2+1))

\int \frac{2}{x 9 x ^{2} + 1} d x

integral of (x^2+5x+7)/(x+3)

\int \frac{x ^{2} + 5 x + 7}{x + 3} d x

inverselaplace (4se^{-3s})/((s^2+4))

in v erse l a pl a ce \frac{4 s e ^{- 3 s}}{( s ^{2} + 4 )}