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} (15 x^{4} - 15 x^{2})

(u^{2} + u)^{3}

csc (3 x) cot (3 x)

\int sin^{3} (x) sin (2 x) d x

y = 2 x^{3} + 3 x^{2} - 12 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)