What is (\partial)/(\partial y)(1/(2-x+y)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial y)(1/(2-x+y))

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

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

Solution steps

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

Treat

x

as a constant

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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