What is (\partial)/(\partial y)(3xy+e^{-x^2y}) ?

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

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