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}{d x} (100 x e^{- 0.5 x})

\frac{\partial}{\partial y} (6 x)

f (x) = x - e^{- x}

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

\frac{\partial}{\partial x} (y \cdot ln (x^{2} + 5 y + 40))

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