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

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

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

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

e^{- y}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= e^{- y} (1 + 0)

Simplify

= e^{- y}

y = x^{2}, y = 2

3 x^{2} y^{^{'}} = y^{^{'}} + 6 x e^{- y}

(e^{4 x^{2}})^{7}

\frac{d x}{d t} = 5 x - 3

12 x

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