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

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

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

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

\frac{y}{2 x + yz}

Solution steps

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

Treat

x, y

as constants

Apply the chain rule:

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

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

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

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

Simplify

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

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

t \to \infty lim (e^{2 t})

\int_{0}^{8} 3 t^{2} - 36 t + 105 d t

x \to 1 lim (g (x))

\int e^{- \frac{1}{2} x} d x

x \to - 1 lim (H (x))

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