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

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

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

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

e^{y} x + 1

Solution steps

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

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} (1)

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

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

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

= x e^{y} + 1 + 0

Simplify

= e^{y} x + 1

\frac{d}{d t} (\frac{6 t + 28}{t + 7})

f (x) = x^{3} (3 - x)^{4}

\frac{d}{d t} (\frac{1}{1 - t})

\int_{0}^{2} (x + 2) d x

y = 2 - x^{2}, y = 10 - 6 x

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