What is (\partial)/(\partial x)(y^2+xy+3y+2x+3) ?

The answer to (\partial)/(\partial x)(y^2+xy+3y+2x+3) is y+2

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(\partial)/(\partial x)(y^2+xy+3y+2x+3)

\frac{\partial}{\partial x} (y^{2} + x y + 3 y + 2 x + 3)

y + 2

Solution steps

\frac{\partial}{\partial x} (y^{2} + x y + 3 y + 2 x + 3)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (y^{2}) + \frac{\partial}{\partial x} (x y) + \frac{\partial}{\partial x} (3 y) + \frac{\partial}{\partial x} (2 x) + \frac{\partial}{\partial x} (3)

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

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

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

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

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

= 0 + y + 0 + 2 + 0

Simplify

= y + 2

What is (\partial)/(\partial x)(y^2+xy+3y+2x+3) ?
The answer to (\partial)/(\partial x)(y^2+xy+3y+2x+3) is y+2