What is the derivative of ((3x-y)/((x+2y))) ?

The derivative of ((3x-y)/((x+2y))) is (-7x\frac{dy)/(dx)+7y}{(x+2y)^2}

What is the first derivative of ((3x-y)/((x+2y))) ?

The first derivative of ((3x-y)/((x+2y))) is (-7x\frac{dy)/(dx)+7y}{(x+2y)^2}

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\frac{d}{d x} (\frac{( 3 x - y )}{( x + 2 y )})

\frac{- 7 x \frac{d y}{d x} + 7 y}{( x + 2 y ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{( 3 x - y )}{( x + 2 y )})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 3 x - y ) ( x + 2 y ) - \frac{d}{d x} ( x + 2 y ) ( 3 x - y )}{( x + 2 y ) ^{2}}

\frac{d}{d x} (3 x - y) = 3 - \frac{d y}{d x}

\frac{d}{d x} (x + 2 y) = 1 + 2 \frac{d y}{d x}

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

Expand

(3 - \frac{d y}{d x}) (x + 2 y) - (1 + 2 \frac{d y}{d x}) (3 x - y) : - 7 x \frac{d y}{d x} + 7 y

= \frac{- 7 x \frac{d y}{d x} + 7 y}{( x + 2 y ) ^{2}}

9 ln (x + 8)

\frac{d}{d q} (\frac{q ^{1} q ^{2}}{r ^{2}})

\frac{d}{d s} (x^{x} - 2^{s} in x)

\frac{x + 4}{x}

y = (x^{2} + 3)^{7}

What is the derivative of ((3x-y)/((x+2y))) ?
The derivative of ((3x-y)/((x+2y))) is (-7x\frac{dy)/(dx)+7y}{(x+2y)^2}
What is the first derivative of ((3x-y)/((x+2y))) ?
The first derivative of ((3x-y)/((x+2y))) is (-7x\frac{dy)/(dx)+7y}{(x+2y)^2}