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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int x^{2} \cdot sin (n x) d x

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

\frac{\partial}{\partial y} (4 x z sin (y))

\frac{d}{d x} (x (x + 13))

(1 + ln (x) + \frac{y}{x}) d x = (9 - ln (x)) d y

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