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

The answer to (\partial)/(\partial y)(x^2+2y^2+3xz) is 4y

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

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

4 y

Solution steps

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

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

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

\frac{\partial}{\partial y} (2 y^{2}) = 4 y

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

= 0 + 4 y + 0

Simplify

= 4 y

What is (\partial)/(\partial y)(x^2+2y^2+3xz) ?
The answer to (\partial)/(\partial y)(x^2+2y^2+3xz) is 4y