What is (\partial)/(\partial x)((z)(xz+yz+xy)) ?

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

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(\partial)/(\partial x)((z)(xz+yz+xy))

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

z (z + y)

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

= z (z + 0 + y)

Simplify

= z (z + y)

\frac{2 x ^{2} + 10 x - 3}{( x + 1 ) ( x ^{2} - 9 )}

(z + i)^{2} \cdot (z - 1)

e^{- 2 x} (x^{2} + x + 1) - 0.5

\frac{d ^{2}}{d ^{2} x} (x^{3} + y^{3} = 16)

\frac{sin ( x ) + cos ^{2} ( x )}{( 1 - sin ( x ) ) ^{2}}

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