What is (\partial)/(\partial x)(sqrt((x+4)/(y+3))) ?

The answer to (\partial)/(\partial x)(sqrt((x+4)/(y+3))) is 1/(2sqrt(x+4)\sqrt{y+3)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(sqrt((x+4)/(y+3)))

\frac{\partial}{\partial x} (\frac{x + 4}{y + 3})

\frac{1}{2 x + 4 y + 3}

Solution steps

\frac{\partial}{\partial x} (\frac{x + 4}{y + 3})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 \frac{x + 4}{y + 3}} \frac{\partial}{\partial x} (\frac{x + 4}{y + 3})

= \frac{1}{2 \frac{x + 4}{y + 3}} \frac{\partial}{\partial x} (\frac{x + 4}{y + 3})

\frac{\partial}{\partial x} (\frac{x + 4}{y + 3}) = \frac{1}{y + 3}

= \frac{1}{2 \frac{x + 4}{y + 3}} \cdot \frac{1}{y + 3}

Simplify

\frac{1}{2 \frac{x + 4}{y + 3}} \cdot \frac{1}{y + 3} : \frac{1}{2 x + 4 y + 3}

= \frac{1}{2 x + 4 y + 3}

What is (\partial)/(\partial x)(sqrt((x+4)/(y+3))) ?
The answer to (\partial)/(\partial x)(sqrt((x+4)/(y+3))) is 1/(2sqrt(x+4)\sqrt{y+3)}