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_{1}^{3} \frac{( 3 x ^{2} - 7 )}{x ^{3}} d x

f (x) = x^{3} e^{4 x}

y^{^{'}} + x (y^{2} + y) = 0, y (2) = 1

\frac{d}{d x} (\frac{( x ^{3} - 4 x ) ^{8}}{8})

x^{2} + 4 x y + x (\frac{d y}{d x}) = 0

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