What is (\partial)/(\partial x)(20sqrt(xy)) ?

The answer to (\partial)/(\partial x)(20sqrt(xy)) is (10sqrt(y))/(sqrt(x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(20sqrt(xy))

\frac{\partial}{\partial x} (20 x y)

\frac{10 y}{x}

Solution steps

\frac{\partial}{\partial x} (20 x y)

Treat

y

as a constant

Take the constant out:

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

= 20 \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

= 20 \cdot \frac{1}{2 x y} y

Simplify

20 \cdot \frac{1}{2 x y} y : \frac{10 y}{x}

= \frac{10 y}{x}

What is (\partial)/(\partial x)(20sqrt(xy)) ?
The answer to (\partial)/(\partial x)(20sqrt(xy)) is (10sqrt(y))/(sqrt(x))