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

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

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

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

x + 2 y

Solution steps

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

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

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

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

= 0 + 2 y + 0 + x

Simplify

= x + 2 y

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