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}}

\int e^{(- 1 - 13 i) t} d t

\int \frac{1}{2 u + 1} d u

x \to 1 + lim (ln (3 x^{2} - x - 2))

f (x) = x^{2} + 1, at x = 3

x \to 3 lim (\frac{5}{( x - 3 ) ^{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)