What is (\partial)/(\partial x)(4xy+yz+5xz-40) ?

The answer to (\partial)/(\partial x)(4xy+yz+5xz-40) is 4y+5z

(\partial)/(\partial x)(4xy+yz+5xz-40)

\frac{\partial}{\partial x} (4 x y + yz + 5 x z - 40)

4 y + 5 z

Solution steps

\frac{\partial}{\partial x} (4 x y + yz + 5 x z - 40)

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (4 x y) + \frac{\partial}{\partial x} (yz) + \frac{\partial}{\partial x} (5 x z) - \frac{\partial}{\partial x} (40)

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

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

\frac{\partial}{\partial x} (5 x z) = 5 z

\frac{\partial}{\partial x} (40) = 0

= 4 y + 0 + 5 z - 0

Simplify

= 4 y + 5 z

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What is (\partial)/(\partial x)(4xy+yz+5xz-40) ?
The answer to (\partial)/(\partial x)(4xy+yz+5xz-40) is 4y+5z