What is the derivative of (-9x-1/(-6x+2)) ?

The derivative of (-9x-1/(-6x+2)) is -6/((3x-1)^2)

What is the first derivative of (-9x-1/(-6x+2)) ?

The first derivative of (-9x-1/(-6x+2)) is -6/((3x-1)^2)

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\frac{d}{d x} (\frac{- 9 x - 1}{- 6 x + 2})

- \frac{6}{( 3 x - 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{- 9 x - 1}{- 6 x + 2})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( - 9 x - 1 ) ( - 6 x + 2 ) - \frac{d}{d x} ( - 6 x + 2 ) ( - 9 x - 1 )}{( - 6 x + 2 ) ^{2}}

\frac{d}{d x} (- 9 x - 1) = - 9

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

= \frac{( - 9 ) ( - 6 x + 2 ) - ( - 6 ) ( - 9 x - 1 )}{( - 6 x + 2 ) ^{2}}

Simplify

\frac{( - 9 ) ( - 6 x + 2 ) - ( - 6 ) ( - 9 x - 1 )}{( - 6 x + 2 ) ^{2}} : - \frac{6}{( 3 x - 1 ) ^{2}}

= - \frac{6}{( 3 x - 1 ) ^{2}}

What is the derivative of (-9x-1/(-6x+2)) ?
The derivative of (-9x-1/(-6x+2)) is -6/((3x-1)^2)
What is the first derivative of (-9x-1/(-6x+2)) ?
The first derivative of (-9x-1/(-6x+2)) is -6/((3x-1)^2)