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

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

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

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

\frac{y}{x}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

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

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

Simplify

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

= \frac{y}{x}

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