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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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

y^{^{'}} + 3 y = 4 e^{- t}

x \to 10 - lim (\frac{1}{x - 10})

\int_{- 1}^{1} \frac{3 x}{( x + 5 ) ^{2}} d x

f (x) = - x^{2} - 4 x - 6, at x = 4

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