What is (\partial)/(\partial x)(((4x-4y))/(4x+4y)) ?

The answer to (\partial)/(\partial x)(((4x-4y))/(4x+4y)) is (2y)/((x+y)^2)

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(\partial)/(\partial x)(((4x-4y))/(4x+4y))

\frac{\partial}{\partial x} (\frac{( 4 x - 4 y )}{4 x + 4 y})

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

Solution steps

\frac{\partial}{\partial x} (\frac{( 4 x - 4 y )}{4 x + 4 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} ( 4 x - 4 y ) ( 4 x + 4 y ) - \frac{\partial}{\partial x} ( 4 x + 4 y ) ( 4 x - 4 y )}{( 4 x + 4 y ) ^{2}}

\frac{\partial}{\partial x} (4 x - 4 y) = 4

\frac{\partial}{\partial x} (4 x + 4 y) = 4

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

Simplify

\frac{4 ( 4 x + 4 y ) - 4 ( 4 x - 4 y )}{( 4 x + 4 y ) ^{2}} : \frac{2 y}{( x + y ) ^{2}}

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

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\frac{\partial}{\partial x} (324 x^{2} - 324 x y + 81 y^{2})

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What is (\partial)/(\partial x)(((4x-4y))/(4x+4y)) ?
The answer to (\partial)/(\partial x)(((4x-4y))/(4x+4y)) is (2y)/((x+y)^2)