What is the derivative of (x^3)/(6x-3) ?

The derivative of (x^3)/(6x-3) is (x^2(4x-3))/(3(2x-1)^2)

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

The first derivative of (x^3)/(6x-3) is (x^2(4x-3))/(3(2x-1)^2)

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derivative of

\frac{x ^{3}}{6 x - 3}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

What is the derivative of (x^3)/(6x-3) ?
The derivative of (x^3)/(6x-3) is (x^2(4x-3))/(3(2x-1)^2)
What is the first derivative of (x^3)/(6x-3) ?
The first derivative of (x^3)/(6x-3) is (x^2(4x-3))/(3(2x-1)^2)