Wang Fang tried to find the derivative of $\frac{x^{5}}{3 x+9}$. Here is her work:

Step 1: This is the quotient of $x^{5}$ and $3 x+9$. So we should use the quotient rule.

Step 2:

$\frac{d}{d x}[\frac{x^{5}}{3 x+9}]=\frac{\frac{d}{d x}[x^{5}]}{\frac{d}{d x}[3 x+9]}$

Step 3: Finding the derivatives of the factors:

$\frac{d}{d x}[x^{5}]=5 x^{4}$

$\frac{d}{d x}[3 x+9]=3$

Step 4: Putting it all together:

$\frac{d}{d x}[\frac{x^{5}}{3 x+9}]=\frac{\frac{d}{d x}[x^{5}]}{\frac{d}{d x}[3 x+9]}=\frac{5 x^{4}}{3}$

Is Wang Fang’s work correct? If not, what’s her mistake?