What is (\partial)/(\partial y)(sqrt(2xy)) ?

The answer to (\partial)/(\partial y)(sqrt(2xy)) is (sqrt(x))/(sqrt(2)\sqrt{y)}

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(\partial)/(\partial y)(sqrt(2xy))

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

\frac{x}{2 y}

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{x}{2 y}

\frac{d}{d x} (\frac{2 π - x cos ( x )}{x - 2 π})

\frac{d}{d x} (7 e^{x^{2} + 1})

\int (5 - x) d x

\frac{1}{s ( s ^{1} + 1 )}

\frac{d}{d x} (2^{3})

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