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

The answer to (\partial)/(\partial y)(-xe^{-3xy}) is 3e^{-3xy}x^2

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= - x e^{- 3 x y} (- 3 x)

Simplify

- x e^{- 3 x y} (- 3 x) : 3 e^{- 3 x y} x^{2}

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

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What is (\partial)/(\partial y)(-xe^{-3xy}) ?
The answer to (\partial)/(\partial y)(-xe^{-3xy}) is 3e^{-3xy}x^2