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

The answer to (\partial)/(\partial x)((2x-y)/(2x+y)) is (4y)/((2x+y)^2)

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

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

\frac{4 y}{( 2 x + y ) ^{2}}

Solution steps

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

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

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

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

Expand

2 (2 x + y) - 2 (2 x - y) : 4 y

= \frac{4 y}{( 2 x + y ) ^{2}}

\frac{d}{d x} (4 x cos (x))

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

\int (\frac{x}{y}) d y

\int_{4}^{\infty} e^{4 x} d x

What is (\partial)/(\partial x)((2x-y)/(2x+y)) ?
The answer to (\partial)/(\partial x)((2x-y)/(2x+y)) is (4y)/((2x+y)^2)