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

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

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

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

y

Solution steps

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

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

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

= y + 0

Simplify

= y

x \to 0 lim (\frac{x - y}{x + y})

f (x) = \frac{x ^{2}}{9 + 4 x}

\int \frac{5}{sin ( x )} d x

4 2 x^{2} + 9

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