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

The answer to (\partial)/(\partial y)(y-e^{-2x^2y}) is 1+2e^{-2yx^2}x^2

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

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

1 + 2 e^{- 2 y x^{2}} x^{2}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (y) = 1

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

= 1 - (- 2 x^{2} e^{- 2 x^{2} y})

Simplify

= 1 + 2 e^{- 2 y x^{2}} x^{2}

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What is (\partial)/(\partial y)(y-e^{-2x^2y}) ?
The answer to (\partial)/(\partial y)(y-e^{-2x^2y}) is 1+2e^{-2yx^2}x^2