What is (\partial)/(\partial x)(sqrt(x*y)) ?

The answer to (\partial)/(\partial x)(sqrt(x*y)) is (sqrt(y))/(2sqrt(x))

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(\partial)/(\partial x)(sqrt(x*y))

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

\frac{y}{2 x}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{y}{2 x}

\int \frac{3 x ^{2}}{1 + x ^{3}} d x

\frac{\partial}{\partial x} (16 - x^{2} - 4 y)

x \to \infty lim (\frac{2}{x !})

\frac{( csc ^{2} ( x ) )}{4}, 4 sin^{2} (x)

\frac{d ^{4}}{d x ^{4}} (cos (x))

What is (\partial)/(\partial x)(sqrt(x*y)) ?
The answer to (\partial)/(\partial x)(sqrt(x*y)) is (sqrt(y))/(2sqrt(x))