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

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

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

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

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

Solution steps

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

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

\frac{\partial}{\partial x} (x + 2 y) = 1

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

Simplify

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

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

\frac{d}{d x} (\frac{sin ( \frac{1}{x} )}{x ^{2}})

x \to - \infty lim (9)

\int (4 - 3 x)^{5} d x

x \to 2 - lim (arcsin (\frac{x}{2}))

\frac{4}{5 s + 1}

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