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

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

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

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

2 x y + z^{2}

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

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

= 2 y x + 0 + z^{2}

Simplify

= 2 x y + z^{2}

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