What is (\partial)/(\partial x)(sqrt((x+5)/(y+5))) ?

The answer to (\partial)/(\partial x)(sqrt((x+5)/(y+5))) is 1/(2sqrt(x+5)\sqrt{y+5)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(sqrt((x+5)/(y+5)))

\frac{\partial}{\partial x} (\frac{x + 5}{y + 5})

\frac{1}{2 x + 5 y + 5}

Solution steps

\frac{\partial}{\partial x} (\frac{x + 5}{y + 5})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 \frac{x + 5}{y + 5}} \frac{\partial}{\partial x} (\frac{x + 5}{y + 5})

= \frac{1}{2 \frac{x + 5}{y + 5}} \frac{\partial}{\partial x} (\frac{x + 5}{y + 5})

\frac{\partial}{\partial x} (\frac{x + 5}{y + 5}) = \frac{1}{y + 5}

= \frac{1}{2 \frac{x + 5}{y + 5}} \cdot \frac{1}{y + 5}

Simplify

\frac{1}{2 \frac{x + 5}{y + 5}} \cdot \frac{1}{y + 5} : \frac{1}{2 x + 5 y + 5}

= \frac{1}{2 x + 5 y + 5}

What is (\partial)/(\partial x)(sqrt((x+5)/(y+5))) ?
The answer to (\partial)/(\partial x)(sqrt((x+5)/(y+5))) is 1/(2sqrt(x+5)\sqrt{y+5)}