What is (\partial)/(\partial y)(sqrt(xy)-z) ?

The answer to (\partial)/(\partial y)(sqrt(xy)-z) is (sqrt(x))/(2sqrt(y))

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(\partial)/(\partial y)(sqrt(xy)-z)

\frac{\partial}{\partial y} (x y - z)

\frac{x}{2 y}

Solution steps

\frac{\partial}{\partial y} (x y - z)

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} (z)

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

\frac{\partial}{\partial y} (z) = 0

= \frac{x}{2 y} - 0

Simplify

= \frac{x}{2 y}

\frac{d ^{2}}{d x ^{2}} (e^{\frac{4}{x}})

\int \frac{3 x}{x ^{2} + 2 x + 5} d x

\int \frac{( 2 x - 3 )}{9 - x ^{2}} d x

y^{^{'}} = - 0.5 y^{1.5}

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

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