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

The answer to (\partial)/(\partial x)(y-e^{-2x^2y}) is 4e^{-2yx^2}yx

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (y) = 0

\frac{\partial}{\partial x} (e^{- 2 x^{2} y}) = - 4 y e^{- 2 y x^{2}} x

= 0 - (- 4 y e^{- 2 y x^{2}} x)

Simplify

= 4 e^{- 2 y x^{2}} y x

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What is (\partial)/(\partial x)(y-e^{-2x^2y}) ?
The answer to (\partial)/(\partial x)(y-e^{-2x^2y}) is 4e^{-2yx^2}yx