What is (\partial)/(\partial x)(((2x-5y))/(2x+5y)) ?

The answer to (\partial)/(\partial x)(((2x-5y))/(2x+5y)) is (20y)/((2x+5y)^2)

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(\partial)/(\partial x)(((2x-5y))/(2x+5y))

\frac{\partial}{\partial x} (\frac{( 2 x - 5 y )}{2 x + 5 y})

\frac{20 y}{( 2 x + 5 y ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{( 2 x - 5 y )}{2 x + 5 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 - 5 y ) ( 2 x + 5 y ) - \frac{\partial}{\partial x} ( 2 x + 5 y ) ( 2 x - 5 y )}{( 2 x + 5 y ) ^{2}}

\frac{\partial}{\partial x} (2 x - 5 y) = 2

\frac{\partial}{\partial x} (2 x + 5 y) = 2

= \frac{2 ( 2 x + 5 y ) - 2 ( 2 x - 5 y )}{( 2 x + 5 y ) ^{2}}

Expand

2 (2 x + 5 y) - 2 (2 x - 5 y) : 20 y

= \frac{20 y}{( 2 x + 5 y ) ^{2}}

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What is (\partial)/(\partial x)(((2x-5y))/(2x+5y)) ?
The answer to (\partial)/(\partial x)(((2x-5y))/(2x+5y)) is (20y)/((2x+5y)^2)