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Beliebt Rechnen >

(\partial)/(\partial y)(3xe^{-1/(y^3)})

Lösung

\frac{\partial}{\partial y} (3 x e^{- \frac{1}{y ^{3}}})

Lösung

\frac{9 e ^{- \frac{1}{y ^{3}}} x}{y ^{4}}

Schritte zur Lösung

\frac{\partial}{\partial y} (3 x e^{- \frac{1}{y ^{3}}})

Behandle

x

als Konstante

Entferne die Konstante:

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

= 3 x \frac{\partial}{\partial y} (e^{- \frac{1}{y ^{3}}})

Wende die Kettenregel an:

e^{- \frac{1}{y ^{3}}} \frac{\partial}{\partial y} (- \frac{1}{y ^{3}})

= e^{- \frac{1}{y ^{3}}} \frac{\partial}{\partial y} (- \frac{1}{y ^{3}})

\frac{\partial}{\partial y} (- \frac{1}{y ^{3}}) = \frac{3}{y ^{4}}

= 3 x e^{- \frac{1}{y ^{3}}} \frac{3}{y ^{4}}

Vereinfache

3 x e^{- \frac{1}{y ^{3}}} \frac{3}{y ^{4}} : \frac{9 e ^{- \frac{1}{y ^{3}}} x}{y ^{4}}

= \frac{9 e ^{- \frac{1}{y ^{3}}} x}{y ^{4}}

Beliebte Beispiele

integral from 115 to 150 of (75)/(2x^2)

\int_{115}^{150} \frac{75}{2 x ^{2}} d x

derivative ((x^2-3x))/(x^2+7x)

d er i v a t i v e \frac{( x ^{2} - 3 x )}{x ^{2} + 7 x}

derivative y=sqrt(9-x)

d er i v a t i v e y = 9 - x

derivative of x(4-x^2^2)

\frac{d}{d x} (x (4 - x^{2})^{2})

integral of 1/(16-x^2)

\int \frac{1}{16 - x ^{2}} d x