What is the derivative of (3x-4/(2x-8)) ?

The derivative of (3x-4/(2x-8)) is -4/((x-4)^2)

What is the first derivative of (3x-4/(2x-8)) ?

The first derivative of (3x-4/(2x-8)) is -4/((x-4)^2)

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\frac{d}{d x} (\frac{3 x - 4}{2 x - 8})

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

Solution steps

\frac{d}{d x} (\frac{3 x - 4}{2 x - 8})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 3 x - 4 ) ( 2 x - 8 ) - \frac{d}{d x} ( 2 x - 8 ) ( 3 x - 4 )}{( 2 x - 8 ) ^{2}}

\frac{d}{d x} (3 x - 4) = 3

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

= \frac{3 ( 2 x - 8 ) - 2 ( 3 x - 4 )}{( 2 x - 8 ) ^{2}}

Simplify

\frac{3 ( 2 x - 8 ) - 2 ( 3 x - 4 )}{( 2 x - 8 ) ^{2}} : - \frac{4}{( x - 4 ) ^{2}}

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

What is the derivative of (3x-4/(2x-8)) ?
The derivative of (3x-4/(2x-8)) is -4/((x-4)^2)
What is the first derivative of (3x-4/(2x-8)) ?
The first derivative of (3x-4/(2x-8)) is -4/((x-4)^2)