What is (\partial)/(\partial x)((z)(xz+xyz-5)) ?

The answer to (\partial)/(\partial x)((z)(xz+xyz-5)) is z(z+zy)

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(\partial)/(\partial x)((z)(xz+xyz-5))

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

z (z + zy)

Solution steps

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

Treat

z, y

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Sum/Difference Rule:

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

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

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

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

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

= z (z + zy - 0)

Simplify

= z (z + zy)

\frac{x ^{3}}{( x - 2 ) ^{2}}

\frac{x ( x - 1 ) ( x + 2 ) ^{2}}{( x + 3 ) ( x - 4 )}

\frac{( 4 x - 1 ) ^{4}}{16}

cos (2 (π - θ))

\frac{1}{2} (u - \frac{1}{2} sin (2 u))

What is (\partial)/(\partial x)((z)(xz+xyz-5)) ?
The answer to (\partial)/(\partial x)((z)(xz+xyz-5)) is z(z+zy)