What is the derivative of ((4x-y)/((2x+y))) ?

The derivative of ((4x-y)/((2x+y))) is (-6x\frac{dy)/(dx)+6y}{(2x+y)^2}

What is the first derivative of ((4x-y)/((2x+y))) ?

The first derivative of ((4x-y)/((2x+y))) is (-6x\frac{dy)/(dx)+6y}{(2x+y)^2}

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

(4 - \frac{d y}{d x}) (2 x + y) - (2 + \frac{d y}{d x}) (4 x - y) : - 6 x \frac{d y}{d x} + 6 y

= \frac{- 6 x \frac{d y}{d x} + 6 y}{( 2 x + y ) ^{2}}

sin (x^{\frac{1}{2}})

(3 + x^{2})^{\frac{1}{2}}

\frac{- x}{( x - 1 )}

\frac{d}{d x} (cos^{2} (y) - sin^{2} (x))

f (x) = (6 x^{2} + 7 x)^{4}

What is the derivative of ((4x-y)/((2x+y))) ?
The derivative of ((4x-y)/((2x+y))) is (-6x\frac{dy)/(dx)+6y}{(2x+y)^2}
What is the first derivative of ((4x-y)/((2x+y))) ?
The first derivative of ((4x-y)/((2x+y))) is (-6x\frac{dy)/(dx)+6y}{(2x+y)^2}