What is (\partial)/(\partial x)(4x^2-4xy+xyz) ?

The answer to (\partial)/(\partial x)(4x^2-4xy+xyz) is 8x-4y+yz

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(\partial)/(\partial x)(4x^2-4xy+xyz)

\frac{\partial}{\partial x} (4 x^{2} - 4 x y + x yz)

8 x - 4 y + yz

Solution steps

\frac{\partial}{\partial x} (4 x^{2} - 4 x y + x yz)

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (4 x^{2}) - \frac{\partial}{\partial x} (4 x y) + \frac{\partial}{\partial x} (x yz)

\frac{\partial}{\partial x} (4 x^{2}) = 8 x

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

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

= 8 x - 4 y + yz

What is (\partial)/(\partial x)(4x^2-4xy+xyz) ?
The answer to (\partial)/(\partial x)(4x^2-4xy+xyz) is 8x-4y+yz