What is (\partial)/(\partial x)((5x-6y)/(5x+6y)) ?

The answer to (\partial)/(\partial x)((5x-6y)/(5x+6y)) is (60y)/((5x+6y)^2)

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(\partial)/(\partial x)((5x-6y)/(5x+6y))

\frac{\partial}{\partial x} (\frac{5 x - 6 y}{5 x + 6 y})

\frac{60 y}{( 5 x + 6 y ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{5 x - 6 y}{5 x + 6 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} ( 5 x - 6 y ) ( 5 x + 6 y ) - \frac{\partial}{\partial x} ( 5 x + 6 y ) ( 5 x - 6 y )}{( 5 x + 6 y ) ^{2}}

\frac{\partial}{\partial x} (5 x - 6 y) = 5

\frac{\partial}{\partial x} (5 x + 6 y) = 5

= \frac{5 ( 5 x + 6 y ) - 5 ( 5 x - 6 y )}{( 5 x + 6 y ) ^{2}}

Expand

5 (5 x + 6 y) - 5 (5 x - 6 y) : 60 y

= \frac{60 y}{( 5 x + 6 y ) ^{2}}

What is (\partial)/(\partial x)((5x-6y)/(5x+6y)) ?
The answer to (\partial)/(\partial x)((5x-6y)/(5x+6y)) is (60y)/((5x+6y)^2)