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

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

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

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

e^{y} - y e^{- x}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

\int (5 x + 7 y) d x

f (x) = 2 sin (x) + x, - π, π

(\frac{2}{( 1 - x ) ^{3}})^{^{'}}

\frac{\partial}{\partial y} (cos (2 y))

\int_{1}^{e} x^{3} \cdot ln (x) d x

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