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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

\frac{x}{2 y}

Solution steps

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

Treat

x

as a constant

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

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

Simplify

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

= \frac{x}{2 y}

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