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

The answer to (\partial)/(\partial x)(((x-3y))/(x+3y)) is (6y)/((x+3y)^2)

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

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

\frac{6 y}{( x + 3 y ) ^{2}}

Solution steps

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

\frac{\partial}{\partial x} (x - 3 y) = 1

\frac{\partial}{\partial x} (x + 3 y) = 1

= \frac{1 \cdot ( x + 3 y ) - 1 \cdot ( x - 3 y )}{( x + 3 y ) ^{2}}

Simplify

\frac{1 \cdot ( x + 3 y ) - 1 \cdot ( x - 3 y )}{( x + 3 y ) ^{2}} : \frac{6 y}{( x + 3 y ) ^{2}}

= \frac{6 y}{( x + 3 y ) ^{2}}

What is (\partial)/(\partial x)(((x-3y))/(x+3y)) ?
The answer to (\partial)/(\partial x)(((x-3y))/(x+3y)) is (6y)/((x+3y)^2)