What is (\partial)/(\partial z)(xy-3xz+yz) ?

The answer to (\partial)/(\partial z)(xy-3xz+yz) is y-3x

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(\partial)/(\partial z)(xy-3xz+yz)

\frac{\partial}{\partial z} (x y - 3 x z + yz)

y - 3 x

Solution steps

\frac{\partial}{\partial z} (x y - 3 x z + yz)

Treat

x, y

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial z} (x y) - \frac{\partial}{\partial z} (3 x z) + \frac{\partial}{\partial z} (yz)

\frac{\partial}{\partial z} (x y) = 0

\frac{\partial}{\partial z} (3 x z) = 3 x

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

= 0 - 3 x + y

Simplify

= y - 3 x

\frac{d ^{3}}{d x ^{3}} (x^{4} - 3 x^{2} + 6 x - 5)

\int - 2 e^{- \frac{x}{2}} d x

\frac{d}{d x} (arctan (\frac{1 - x}{1 + x}))

x^{- 2}, 3

\frac{d}{d s} (\frac{k}{s ^{2} + k ^{2}})

What is (\partial)/(\partial z)(xy-3xz+yz) ?
The answer to (\partial)/(\partial z)(xy-3xz+yz) is y-3x