What is (\partial)/(\partial x)(6xy+5yz+xz) ?

The answer to (\partial)/(\partial x)(6xy+5yz+xz) is 6y+z

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(\partial)/(\partial x)(6xy+5yz+xz)

\frac{\partial}{\partial x} (6 x y + 5 yz + x z)

6 y + z

Solution steps

\frac{\partial}{\partial x} (6 x y + 5 yz + x z)

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (6 x y) + \frac{\partial}{\partial x} (5 yz) + \frac{\partial}{\partial x} (x z)

\frac{\partial}{\partial x} (6 x y) = 6 y

\frac{\partial}{\partial x} (5 yz) = 0

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

= 6 y + 0 + z

Simplify

= 6 y + z

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What is (\partial)/(\partial x)(6xy+5yz+xz) ?
The answer to (\partial)/(\partial x)(6xy+5yz+xz) is 6y+z