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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

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

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