What is (\partial)/(\partial x)(sqrt(1+xy)) ?

The answer to (\partial)/(\partial x)(sqrt(1+xy)) is y/(2sqrt(1+xy))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(sqrt(1+xy))

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

What is (\partial)/(\partial x)(sqrt(1+xy)) ?
The answer to (\partial)/(\partial x)(sqrt(1+xy)) is y/(2sqrt(1+xy))