What is (\partial)/(\partial y)(xe^y+y) ?

The answer to (\partial)/(\partial y)(xe^y+y) is xe^y+1

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(\partial)/(\partial y)(xe^y+y)

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

x e^{y} + 1

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= x e^{y} + 1

\frac{d y}{d x} = x y^{\frac{1}{2}}

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

\int \frac{( x ^{2} - 25 ) ^{\frac{3}{2}}}{x ^{6}} d x

\frac{6 ( x ^{4} - 2 )}{x ^{3}}

(5 x^{2} + 8)^{8}

What is (\partial)/(\partial y)(xe^y+y) ?
The answer to (\partial)/(\partial y)(xe^y+y) is xe^y+1