\[\frac{d}{dx} \frac{{x}^{2}}{3x-1}\]
1
Use Quotient Rule to find the derivative of x23x−1\frac{{x}^{2}}{3x-1}. The quotient rule states that (fg)′=f′g−fg′g2(\frac{f}{g})'=\frac{f'g-fg'}{{g}^{2}}.
(3x−1)(ddxx2)−x2(ddx3x−1)(3x−1)2\frac{(3x-1)(\frac{d}{dx} {x}^{2})-{x}^{2}(\frac{d}{dx} 3x-1)}{{(3x-1)}^{2}}

2
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
2x(3x−1)−x2(ddx3x−1)(3x−1)2\frac{2x(3x-1)-{x}^{2}(\frac{d}{dx} 3x-1)}{{(3x-1)}^{2}}

3
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
3x2−2x(3x−1)2\frac{3{x}^{2}-2x}{{(3x-1)}^{2}}

Done
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