What is (\partial)/(\partial y)(sqrt(x+yz)) ?

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

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(\partial)/(\partial y)(sqrt(x+yz))

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

\frac{z}{2 x + yz}

Solution steps

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

Treat

x, z

as constants

Apply the chain rule:

\frac{1}{2 x + yz} \frac{\partial}{\partial y} (x + yz)

= \frac{1}{2 x + yz} \frac{\partial}{\partial y} (x + yz)

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

= \frac{1}{2 x + yz} z

Simplify

\frac{1}{2 x + yz} z : \frac{z}{2 x + yz}

= \frac{z}{2 x + yz}

\frac{d}{d x} (x^{2} x^{2} - 9)

x \to 12 lim (\frac{x ^{3}}{3})

\frac{\partial}{\partial y} (x + y - 320)

\frac{\partial}{\partial x} (x^{4} + y^{3})

\frac{1}{1 + x}, 0

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