What is (\partial)/(\partial x)(((2x-y))/(5x+3y)) ?

The answer to (\partial)/(\partial x)(((2x-y))/(5x+3y)) is (11y)/((5x+3y)^2)

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(\partial)/(\partial x)(((2x-y))/(5x+3y))

\frac{\partial}{\partial x} (\frac{( 2 x - y )}{5 x + 3 y})

\frac{11 y}{( 5 x + 3 y ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{( 2 x - y )}{5 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} ( 2 x - y ) ( 5 x + 3 y ) - \frac{\partial}{\partial x} ( 5 x + 3 y ) ( 2 x - y )}{( 5 x + 3 y ) ^{2}}

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

\frac{\partial}{\partial x} (5 x + 3 y) = 5

= \frac{2 ( 5 x + 3 y ) - 5 ( 2 x - y )}{( 5 x + 3 y ) ^{2}}

Expand

2 (5 x + 3 y) - 5 (2 x - y) : 11 y

= \frac{11 y}{( 5 x + 3 y ) ^{2}}

What is (\partial)/(\partial x)(((2x-y))/(5x+3y)) ?
The answer to (\partial)/(\partial x)(((2x-y))/(5x+3y)) is (11y)/((5x+3y)^2)