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

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

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

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

\frac{y}{2 x}

Solution steps

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

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} (z)

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

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

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

Simplify

= \frac{y}{2 x}

f (x) = 7 x^{2}

(- 5, 2), (5, 6)

t^{\frac{1}{2}}

\frac{d}{d x} (tan (\frac{y}{x}))

x \to 6 lim (\frac{x ^{2} + 11 x - 30}{x ^{2} - 13 x - 42})

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