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

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

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(\partial)/(\partial z)(xy+yz+zx)

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

x + y

Solution steps

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

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} (z x)

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

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

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

= 0 + y + x

Simplify

= x + y

\frac{d}{d x} (x cos^{3} (x))

\int_{1}^{2} x ln (x) d x

\frac{d}{d x} (e^{(- 3 x)})

e^{- 3 z + 1} + 8

x^{\frac{2}{3}} + y^{\frac{2}{3}} = 5, (1, 8)

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