What is the derivative of ((2x-1^3)/((x-3)^2)) ?

The derivative of ((2x-1^3)/((x-3)^2)) is (2(2x-1)^2(x-8))/((x-3)^3)

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

The first derivative of ((2x-1^3)/((x-3)^2)) is (2(2x-1)^2(x-8))/((x-3)^3)

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

\frac{2 ( 2 x - 1 ) ^{2} ( x - 8 )}{( x - 3 ) ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{6 ( 2 x - 1 ) ^{2} ( x - 3 ) ^{2} - 2 ( x - 3 ) ( 2 x - 1 ) ^{3}}{( ( x - 3 ) ^{2} ) ^{2}} : \frac{2 ( 2 x - 1 ) ^{2} ( x - 8 )}{( x - 3 ) ^{3}}

= \frac{2 ( 2 x - 1 ) ^{2} ( x - 8 )}{( x - 3 ) ^{3}}

What is the derivative of ((2x-1^3)/((x-3)^2)) ?
The derivative of ((2x-1^3)/((x-3)^2)) is (2(2x-1)^2(x-8))/((x-3)^3)
What is the first derivative of ((2x-1^3)/((x-3)^2)) ?
The first derivative of ((2x-1^3)/((x-3)^2)) is (2(2x-1)^2(x-8))/((x-3)^3)