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

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

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

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

2 e^{- y} x

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (x^{2}) = 2 x

\frac{\partial}{\partial x} (y^{2}) = 0

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

Simplify

= 2 e^{- y} x

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