What is (\partial)/(\partial y)(xe^y-x^5+y-3) ?

The answer to (\partial)/(\partial y)(xe^y-x^5+y-3) is e^yx+1

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(\partial)/(\partial y)(xe^y-x^5+y-3)

\frac{\partial}{\partial y} (x e^{y} - x^{5} + y - 3)

e^{y} x + 1

Solution steps

\frac{\partial}{\partial y} (x e^{y} - x^{5} + y - 3)

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} (x^{5}) + \frac{\partial}{\partial y} (y) - \frac{\partial}{\partial y} (3)

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

\frac{\partial}{\partial y} (x^{5}) = 0

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

\frac{\partial}{\partial y} (3) = 0

= x e^{y} - 0 + 1 - 0

Simplify

= e^{y} x + 1

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What is (\partial)/(\partial y)(xe^y-x^5+y-3) ?
The answer to (\partial)/(\partial y)(xe^y-x^5+y-3) is e^yx+1