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

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

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

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

y

Solution steps

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

Simplify

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

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (2 yz) = 0

= y + 0

Simplify

= y

n = 0 \sum \infty \frac{3 ^{n}}{5 ^{n}}

y = 6 sin (x), at x = \frac{π}{6}

\frac{\partial}{\partial y} (x y - \frac{x ^{4}}{4})

\int e^{- 2 x} sin (6 x) d x

\frac{d}{d x} (x^{6} e^{2.5 x})

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