What is (\partial)/(\partial y)(xy+yz+zx) ?

The answer to (\partial)/(\partial y)(xy+yz+zx) is x+z

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(\partial)/(\partial y)(xy+yz+zx)

\frac{\partial}{\partial y} (x y + yz + z x)

x + z

Solution steps

\frac{\partial}{\partial y} (x y + yz + z x)

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial y} (yz) = z

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

= x + z + 0

Simplify

= x + z

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