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}}

g (u) = u + 1 (1 - 8 u^{2})^{7}

\frac{d}{d x} (ln (1 + \frac{ln ( 2 )}{x}))

\int_{0}^{2} 2 x^{2} - x^{3} d x

\frac{d}{d x} (2 x^{2} + 4 x + 3)

\int \frac{x - 1}{( x ^{2} + 4 x + 5 ) ^{2}} d x

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