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

The answer to (\partial)/(\partial y)(3xe^{-1/(y^3)}) is (9e^{-1/(y^3)}x)/(y^4)

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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}}

Simplify

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}}

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What is (\partial)/(\partial y)(3xe^{-1/(y^3)}) ?
The answer to (\partial)/(\partial y)(3xe^{-1/(y^3)}) is (9e^{-1/(y^3)}x)/(y^4)