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

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

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

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

x^{2} + 2 yz

Solution steps

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

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

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

= x^{2} + 2 zy + 0

Simplify

= x^{2} + 2 yz

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