What is the derivative of (-8x-2/(9x-4)) ?

The derivative of (-8x-2/(9x-4)) is (50)/((9x-4)^2)

What is the first derivative of (-8x-2/(9x-4)) ?

The first derivative of (-8x-2/(9x-4)) is (50)/((9x-4)^2)

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\frac{d}{d x} (\frac{- 8 x - 2}{9 x - 4})

\frac{50}{( 9 x - 4 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{- 8 x - 2}{9 x - 4})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( - 8 x - 2 ) ( 9 x - 4 ) - \frac{d}{d x} ( 9 x - 4 ) ( - 8 x - 2 )}{( 9 x - 4 ) ^{2}}

\frac{d}{d x} (- 8 x - 2) = - 8

\frac{d}{d x} (9 x - 4) = 9

= \frac{( - 8 ) ( 9 x - 4 ) - 9 ( - 8 x - 2 )}{( 9 x - 4 ) ^{2}}

Simplify

\frac{( - 8 ) ( 9 x - 4 ) - 9 ( - 8 x - 2 )}{( 9 x - 4 ) ^{2}} : \frac{50}{( 9 x - 4 ) ^{2}}

= \frac{50}{( 9 x - 4 ) ^{2}}

What is the derivative of (-8x-2/(9x-4)) ?
The derivative of (-8x-2/(9x-4)) is (50)/((9x-4)^2)
What is the first derivative of (-8x-2/(9x-4)) ?
The first derivative of (-8x-2/(9x-4)) is (50)/((9x-4)^2)