What is (\partial)/(\partial x)((7x-4y)/(7x+4y)) ?

The answer to (\partial)/(\partial x)((7x-4y)/(7x+4y)) is (56y)/((7x+4y)^2)

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(\partial)/(\partial x)((7x-4y)/(7x+4y))

\frac{\partial}{\partial x} (\frac{7 x - 4 y}{7 x + 4 y})

\frac{56 y}{( 7 x + 4 y ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{7 x - 4 y}{7 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} ( 7 x - 4 y ) ( 7 x + 4 y ) - \frac{\partial}{\partial x} ( 7 x + 4 y ) ( 7 x - 4 y )}{( 7 x + 4 y ) ^{2}}

\frac{\partial}{\partial x} (7 x - 4 y) = 7

\frac{\partial}{\partial x} (7 x + 4 y) = 7

= \frac{7 ( 7 x + 4 y ) - 7 ( 7 x - 4 y )}{( 7 x + 4 y ) ^{2}}

Expand

7 (7 x + 4 y) - 7 (7 x - 4 y) : 56 y

= \frac{56 y}{( 7 x + 4 y ) ^{2}}

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What is (\partial)/(\partial x)((7x-4y)/(7x+4y)) ?
The answer to (\partial)/(\partial x)((7x-4y)/(7x+4y)) is (56y)/((7x+4y)^2)