What is (\partial)/(\partial x)(((4x-4y))/(4x+3y)) ?

The answer to (\partial)/(\partial x)(((4x-4y))/(4x+3y)) is (28y)/((4x+3y)^2)

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(\partial)/(\partial x)(((4x-4y))/(4x+3y))

\frac{\partial}{\partial x} (\frac{( 4 x - 4 y )}{4 x + 3 y})

\frac{28 y}{( 4 x + 3 y ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{( 4 x - 4 y )}{4 x + 3 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 + 3 y ) - \frac{\partial}{\partial x} ( 4 x + 3 y ) ( 4 x - 4 y )}{( 4 x + 3 y ) ^{2}}

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

\frac{\partial}{\partial x} (4 x + 3 y) = 4

= \frac{4 ( 4 x + 3 y ) - 4 ( 4 x - 4 y )}{( 4 x + 3 y ) ^{2}}

Expand

4 (4 x + 3 y) - 4 (4 x - 4 y) : 28 y

= \frac{28 y}{( 4 x + 3 y ) ^{2}}

What is (\partial)/(\partial x)(((4x-4y))/(4x+3y)) ?
The answer to (\partial)/(\partial x)(((4x-4y))/(4x+3y)) is (28y)/((4x+3y)^2)