What is (\partial)/(\partial y)(x^2y+x+y) ?

The answer to (\partial)/(\partial y)(x^2y+x+y) is x^2+1

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(\partial)/(\partial y)(x^2y+x+y)

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

x^{2} + 1

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (x^{2} y) + \frac{\partial}{\partial y} (x) + \frac{\partial}{\partial y} (y)

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

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

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

= x^{2} + 0 + 1

Simplify

= x^{2} + 1

What is (\partial)/(\partial y)(x^2y+x+y) ?
The answer to (\partial)/(\partial y)(x^2y+x+y) is x^2+1