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

Simplify

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

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

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