What is the derivative of (3x-1)/((x-1)^3) ?

The derivative of (3x-1)/((x-1)^3) is -(6x)/((x-1)^4)

What is the first derivative of (3x-1)/((x-1)^3) ?

The first derivative of (3x-1)/((x-1)^3) is -(6x)/((x-1)^4)

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derivative of

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

- \frac{6 x}{( x - 1 ) ^{4}}

Solution steps

\frac{d}{d x} (\frac{3 x - 1}{( x - 1 ) ^{3}})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (3 x - 1) = 3

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

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

Simplify

\frac{3 ( x - 1 ) ^{3} - 3 ( x - 1 ) ^{2} ( 3 x - 1 )}{( ( x - 1 ) ^{3} ) ^{2}} : - \frac{6 x}{( x - 1 ) ^{4}}

= - \frac{6 x}{( x - 1 ) ^{4}}

What is the derivative of (3x-1)/((x-1)^3) ?
The derivative of (3x-1)/((x-1)^3) is -(6x)/((x-1)^4)
What is the first derivative of (3x-1)/((x-1)^3) ?
The first derivative of (3x-1)/((x-1)^3) is -(6x)/((x-1)^4)