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

The answer to (\partial)/(\partial x)(((3x-y))/((x+2y))) is (7y)/((x+2y)^2)

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

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

\frac{7 y}{( x + 2 y ) ^{2}}

Solution steps

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

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

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

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

Simplify

\frac{3 ( x + 2 y ) - 1 \cdot ( 3 x - y )}{( x + 2 y ) ^{2}} : \frac{7 y}{( x + 2 y ) ^{2}}

= \frac{7 y}{( x + 2 y ) ^{2}}

\int \frac{7 x ^{2} + 2 x - 7}{x ^{3} - x} d x

\frac{d y}{d x} + y = y^{2}

\int x \cdot e^{1 - x^{2}} d x

\int \frac{( e ^{x} + 1 ) ^{2}}{e ^{x}} d x

\frac{d}{d x} (\frac{1}{27} (2 x - 1)^{3} (6 - 3 x) + 1)

What is (\partial)/(\partial x)(((3x-y))/((x+2y))) ?
The answer to (\partial)/(\partial x)(((3x-y))/((x+2y))) is (7y)/((x+2y)^2)