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

The answer to (\partial)/(\partial x)((-4)/(x+y)) is 4/((x+y)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)((-4)/(x+y))

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

\frac{4}{( x + y ) ^{2}}

Solution steps

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

Simplify

\frac{- 4}{x + y} : - \frac{4}{x + y}

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

Treat

y

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

= - 4 (- \frac{1}{( x + y ) ^{2}} \cdot 1)

Simplify

- 4 (- \frac{1}{( x + y ) ^{2}} \cdot 1) : \frac{4}{( x + y ) ^{2}}

= \frac{4}{( x + y ) ^{2}}

What is (\partial)/(\partial x)((-4)/(x+y)) ?
The answer to (\partial)/(\partial x)((-4)/(x+y)) is 4/((x+y)^2)