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

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

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

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

\frac{x}{y}

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{x}{y}

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y^{^{''}} - 9 y^{^{'}} + 18 y = 2 sin (5 t)

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