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

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

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

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

x + 2 y + 1

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (x^{2}) = 0

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

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

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

= 0 + x + 2 y + 1

Simplify

= x + 2 y + 1

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