What is (\partial)/(\partial x)((4x-y)/(4x+y)) ?

The answer to (\partial)/(\partial x)((4x-y)/(4x+y)) is (8y)/((4x+y)^2)

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(\partial)/(\partial x)((4x-y)/(4x+y))

\frac{\partial}{\partial x} (\frac{4 x - y}{4 x + y})

\frac{8 y}{( 4 x + y ) ^{2}}

Solution steps

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

\frac{\partial}{\partial x} (4 x - y) = 4

\frac{\partial}{\partial x} (4 x + y) = 4

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

Expand

4 (4 x + y) - 4 (4 x - y) : 8 y

= \frac{8 y}{( 4 x + y ) ^{2}}

\frac{d y}{d x} = y^{- 1} x^{- 3}

y^{^{'}} = \frac{6 y ^{2}}{x ^{2}}, y (- 2) = 5

\frac{d}{d x} (\frac{4}{3} tan (x))

x \to - 1 lim (13 + x)

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

What is (\partial)/(\partial x)((4x-y)/(4x+y)) ?
The answer to (\partial)/(\partial x)((4x-y)/(4x+y)) is (8y)/((4x+y)^2)