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Beliebt Rechnen >

(\partial)/(\partial y)(x^2e^{-x/y})

Lösung

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

Lösung

\frac{e ^{- \frac{x}{y}} x ^{3}}{y ^{2}}

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

e^{- \frac{x}{y}} \frac{\partial}{\partial y} (- \frac{x}{y})

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

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

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

Vereinfache

x^{2} e^{- \frac{x}{y}} \frac{x}{y ^{2}} : \frac{e ^{- \frac{x}{y}} x ^{3}}{y ^{2}}

= \frac{e ^{- \frac{x}{y}} x ^{3}}{y ^{2}}

Beliebte Beispiele

integral of 13e^u

\int 13 e^{u} d u

tangent f(x)=x^2-3x+5,\at x=2

t an g e n t f (x) = x^{2} - 3 x + 5, at x = 2

y^'= y/x+sqrt(1+(y/x)^2)

y^{^{'}} = \frac{y}{x} + 1 + (\frac{y}{x})^{2}

integral of (x^2-12)/(x^3+4x)

\int \frac{x ^{2} - 12}{x ^{3} + 4 x} d x

(\partial)/(\partial x)((2xy+3)e^{-xy})

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