What is (\partial)/(\partial x)(3xy+4xz+5yz-3) ?

The answer to (\partial)/(\partial x)(3xy+4xz+5yz-3) is 3y+4z

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(\partial)/(\partial x)(3xy+4xz+5yz-3)

\frac{\partial}{\partial x} (3 x y + 4 x z + 5 yz - 3)

3 y + 4 z

Solution steps

\frac{\partial}{\partial x} (3 x y + 4 x z + 5 yz - 3)

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (3 x y) + \frac{\partial}{\partial x} (4 x z) + \frac{\partial}{\partial x} (5 yz) - \frac{\partial}{\partial x} (3)

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

\frac{\partial}{\partial x} (4 x z) = 4 z

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

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

= 3 y + 4 z + 0 - 0

Simplify

= 3 y + 4 z

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What is (\partial)/(\partial x)(3xy+4xz+5yz-3) ?
The answer to (\partial)/(\partial x)(3xy+4xz+5yz-3) is 3y+4z