What is (\partial)/(\partial x)((1+x)/(x+y)) ?

The answer to (\partial)/(\partial x)((1+x)/(x+y)) is (y-1)/((x+y)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)((1+x)/(x+y))

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

\frac{y - 1}{( x + y ) ^{2}}

Solution steps

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

Treat

y

as a constant

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

= \frac{1 \cdot ( x + y ) - 1 \cdot ( 1 + x )}{( x + y ) ^{2}}

Simplify

\frac{1 \cdot ( x + y ) - 1 \cdot ( 1 + x )}{( x + y ) ^{2}} : \frac{y - 1}{( x + y ) ^{2}}

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

\int t^{2} + t d t

\int x - 2 y

- \frac{1}{s ( s - 1 ) ( 2 s + 1 ) ( s + 2 )}

\int_{0}^{7} 2 π x (7 x - x^{2}) d x

3 \frac{d y}{d x} + 5 y = 1

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