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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

= 2 \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

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

Simplify

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

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

d er i v a t i v e \frac{x}{x + 9}

\frac{d}{d x} (\frac{1}{( 1 - x ) ^{2}})

\int_{0}^{1} \frac{x}{( x + 1 ) ( x ^{2} + 1 )} d x

\int x (x - 5)^{2} d x

d er i v a t i v e f (x) = \frac{x ^{3}}{24} + \frac{2}{x}

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