Consider the function $f(x)=\frac{3x^{3}9}{x^{\frac{4}{3}}}.$ Complete parts $($a$)$ through $($c$)$ below.

$($a$)$ Find the derivative using the quotient rule. Let $u(x)=3x^{3}9$ and $v(x)=x^{\frac{?}{\text{b}\text{a}\text{r}}(3)}.$ How is the derivative of a quotient of two functions defined?

A$.f^{\text{'}}(x)=\frac{v(x)*u(x)-u^{\text{'}}(x)*v^{\text{'}}(x)}{[v(x){]}^2}$

B$.f^{\text{'}}(x)=\frac{v^{\text{'}}(x)*u^{\text{'}}(x)-u(x)*v(x)}{[v(x){]}^2}$

c$.f^{\text{'}}(x)=\frac{v^{\text{'}}(x)*u(x)-u^{\text{'}}(x)*v(x)}{[v(x){]}^2}$

D$.f^{\text{'}}(x)=\frac{v(x)*u^{\text{'}}(x)-u(x)*v^{\text{'}}(x)}{[v(x){]}^2}$

The derivative is $f^{\text{'}}(x)=$

$($b$)$ Find the derivative by first simplifying the function to $f(x)=\frac{3x^3}{x^{\frac{4}{3}}}\frac{9}{x^{\frac{4}{3}}}=3x^{\frac{5}{3}}9x^{-\frac{4}{3}}$ and using the power and sum$/$difference rules.

The derivative is $f^{\text{'}}(x)=$

$($c$)$ Compare your answers from parts $($a$)$ and $($b$)$ and explain any discrepancies.

A$.$ The expressions in parts $($a$)$ and $($b$)$ are equivalent

B$.$ The expressions in parts $($a$)$ and $($b$)$ are not equivalent. The derivative in part $($a$)$ has an expression in the denominator, while the answer in part $($b$)$ does not.