If you want to avoid using the quotient rule, you can cancel the powers of x :
[tex]h(x) = \frac{2x ^{4} \cot(x) }{3 {x}^{2} } = \frac{2}{3} {x}^{2} \cot(x) [/tex]
Then differentiate using the product rule.
[tex]h'(x)=\frac23\left(2x\cot(x)-x^2\csc^2(x)\right)[/tex]
[tex]h'(x)=\frac43x\cot(x)-\frac23x^2\csc^2(x)[/tex]
