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

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

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

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

y - x

Solution steps

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

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

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

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

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

= 0 + y - x

Simplify

= y - x

1 - y^{2} d x = 1 - x^{2} d y

\int_{0}^{2} \frac{2 x}{( x ^{2} + 5 ) ^{3}} d x

x \to 0 lim (\frac{- 2 e ^{- x}}{2 x - 2})

\int \frac{e ^{4 x}}{- 4 x} d x

x \to + 0 lim (\frac{( 3 e ^{x} - 3 )}{x})

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