What is (\partial)/(\partial x)(xe^y+y+1) ?

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

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(\partial)/(\partial x)(xe^y+y+1)

\frac{\partial}{\partial x} (x e^{y} + y + 1)

e^{y}

Solution steps

\frac{\partial}{\partial x} (x e^{y} + y + 1)

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

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

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

\frac{\partial}{\partial x} (1) = 0

= e^{y} + 0 + 0

Simplify

= e^{y}

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

\int_{0}^{0.02} 200 x d x

\frac{3 s + 1}{s ( s + 2 )}

\frac{1}{2 x + 2}, at x = 5

(4 - x^{2}) \frac{d y}{d x} = 2 y

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