What is (\partial)/(\partial y)(xy+yz+zy) ?

The answer to (\partial)/(\partial y)(xy+yz+zy) is x+2z

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(\partial)/(\partial y)(xy+yz+zy)

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

x + 2 z

Solution steps

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

Simplify

x y + yz + zy : x y + 2 yz

= \frac{\partial}{\partial y} (x y + 2 yz)

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (x y) + \frac{\partial}{\partial y} (2 yz)

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

\frac{\partial}{\partial y} (2 yz) = 2 z

= x + 2 z

f (x) = - \frac{1}{9} (x^{- 9} - x^{18})

\int \frac{1}{16 e ^{- 5 x} + e ^{5 x}} d x

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\int 4 x^{7} d x

What is (\partial)/(\partial y)(xy+yz+zy) ?
The answer to (\partial)/(\partial y)(xy+yz+zy) is x+2z