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

The answer to (\partial)/(\partial x)((3x-5y)/(3x+5y)) is (30y)/((3x+5y)^2)

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

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

\frac{30 y}{( 3 x + 5 y ) ^{2}}

Solution steps

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

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

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

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

Expand

3 (3 x + 5 y) - 3 (3 x - 5 y) : 30 y

= \frac{30 y}{( 3 x + 5 y ) ^{2}}

What is (\partial)/(\partial x)((3x-5y)/(3x+5y)) ?
The answer to (\partial)/(\partial x)((3x-5y)/(3x+5y)) is (30y)/((3x+5y)^2)