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

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

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

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

2 e^{- y} x

Solution steps

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

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

y^{^{'}} = \frac{2 x y}{x ^{2} - y ^{2}}, y (1) = 1

y = (x^{5} + 1)^{8}

\int 2 x + 2 x^{- 2} d x

\int \frac{x}{6 + π} d x

\frac{d}{d x} ((x^{2}) \cdot ln (x))

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