What is (\partial)/(\partial x)(y^2(x+y)^{-2}) ?

The answer to (\partial)/(\partial x)(y^2(x+y)^{-2}) is -(2y^2)/((x+y)^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

- \frac{2 y ^{2}}{( x + y ) ^{3}}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

- \frac{2}{( x + y ) ^{3}} \frac{\partial}{\partial x} (x + y)

= - \frac{2}{( x + y ) ^{3}} \frac{\partial}{\partial x} (x + y)

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

= y^{2} (- \frac{2}{( x + y ) ^{3}} \cdot 1)

Simplify

y^{2} (- \frac{2}{( x + y ) ^{3}} \cdot 1) : - \frac{2 y ^{2}}{( x + y ) ^{3}}

= - \frac{2 y ^{2}}{( x + y ) ^{3}}

What is (\partial)/(\partial x)(y^2(x+y)^{-2}) ?
The answer to (\partial)/(\partial x)(y^2(x+y)^{-2}) is -(2y^2)/((x+y)^3)