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

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

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(\partial)/(\partial y)(x^2y+x+1)

\frac{\partial}{\partial y} (x^{2} y + x + 1)

x^{2}

Solution steps

\frac{\partial}{\partial y} (x^{2} y + x + 1)

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} (1)

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

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

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

= x^{2} + 0 + 0

Simplify

= x^{2}

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