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

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

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

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

x (x + x y)

Solution steps

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

Treat

x, y

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

= x (x + x y - 0)

Simplify

= x (x + x y)

(e^{2 x} - 6)^{2}

\frac{x}{( 5 x - 4 ) ^{2}}

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

\frac{( 2 x - y ) d x}{( x + 4 y ) d y}

\frac{1}{( z - 1 ) ^{2} ( z - 3 )}

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