What is (\partial)/(\partial x)((2x-2y)/(2x+2y)) ?

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

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(\partial)/(\partial x)((2x-2y)/(2x+2y))

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

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

Solution steps

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

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

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

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

Simplify

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

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

f (x) = \frac{9}{x}, at x = 2

\int_{1}^{5} x^{2} d x

\frac{d ^{2} y}{d x ^{2}} + y = 1 + x

\int (4 x^{3} - 9 x^{2} + 7 x) e^{- x} d x

\frac{d}{d x} (7 x - 2)

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