What is the d/(dy)((4x-2y)/(4x+2y)) ?

The d/(dy)((4x-2y)/(4x+2y)) is -(4x)/((2x+y)^2)

What is the first d/(dy)((4x-2y)/(4x+2y)) ?

The first d/(dy)((4x-2y)/(4x+2y)) is -(4x)/((2x+y)^2)

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

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

Solution steps

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

Treat

x

as a constant

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

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

\frac{d}{d x} (r (x) (x)^{2} - x^{2})

\frac{d}{d x} ((1 + e^{x})^{3})

e^{- 2 t} cos (3 t)

\frac{\partial}{\partial x} (x e^{y} + x^{4} y + y^{3})

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

What is the d/(dy)((4x-2y)/(4x+2y)) ?
The d/(dy)((4x-2y)/(4x+2y)) is -(4x)/((2x+y)^2)
What is the first d/(dy)((4x-2y)/(4x+2y)) ?
The first d/(dy)((4x-2y)/(4x+2y)) is -(4x)/((2x+y)^2)