What is (\partial)/(\partial x)(sqrt((x+4)/(y+5))) ?

The answer to (\partial)/(\partial x)(sqrt((x+4)/(y+5))) is 1/(2sqrt(x+4)\sqrt{y+5)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(sqrt((x+4)/(y+5)))

\frac{\partial}{\partial x} (\frac{x + 4}{y + 5})

\frac{1}{2 x + 4 y + 5}

Solution steps

\frac{\partial}{\partial x} (\frac{x + 4}{y + 5})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 \frac{x + 4}{y + 5}} \frac{\partial}{\partial x} (\frac{x + 4}{y + 5})

= \frac{1}{2 \frac{x + 4}{y + 5}} \frac{\partial}{\partial x} (\frac{x + 4}{y + 5})

\frac{\partial}{\partial x} (\frac{x + 4}{y + 5}) = \frac{1}{y + 5}

= \frac{1}{2 \frac{x + 4}{y + 5}} \cdot \frac{1}{y + 5}

Simplify

\frac{1}{2 \frac{x + 4}{y + 5}} \cdot \frac{1}{y + 5} : \frac{1}{2 x + 4 y + 5}

= \frac{1}{2 x + 4 y + 5}

y^{^{'}} = \frac{y}{x ln ( x )}

110 x - 16 x^{2}

\frac{d}{d x} (16)

\int \frac{7 - 6 x ^{3} + 4 x ^{6}}{x ^{6}} d x

\frac{d}{d x} (arctan (\frac{1}{3 x}))

What is (\partial)/(\partial x)(sqrt((x+4)/(y+5))) ?
The answer to (\partial)/(\partial x)(sqrt((x+4)/(y+5))) is 1/(2sqrt(x+4)\sqrt{y+5)}