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AP®︎ Calculus AB (2017 edition)

Course: AP®︎ Calculus AB (2017 edition)>Unit 3

Lesson 12: Strategy in differentiating functions

Differentiating functions: Find the error

AP.CALC: FUN‑3 (EU)

Problem

Wang Fang tried to find the derivative of start fraction, x, start superscript, 5, end superscript, divided by, 3, x, plus, 9, end fraction. Here is her work:
Step 1: This is the quotient of x, start superscript, 5, end superscript and 3, x, plus, 9. So we should use the quotient rule.
Step 2:
start fraction, d, divided by, d, x, end fraction, open bracket, start fraction, x, start superscript, 5, end superscript, divided by, 3, x, plus, 9, end fraction, close bracket, equals, start fraction, start fraction, d, divided by, d, x, end fraction, open bracket, x, start superscript, 5, end superscript, close bracket, divided by, start fraction, d, divided by, d, x, end fraction, open bracket, 3, x, plus, 9, close bracket, end fraction
Step 3: Finding the derivatives of the factors:
\begin{aligned} \dfrac{d}{dx}[x^5]&=5x^4 \\\\ \dfrac{d}{dx}[3x+9]&=3 \end{aligned}
Step 4: Putting it all together:
\begin{aligned} &\phantom{=}\dfrac{d}{dx} \left[ \dfrac{x^5}{3x+9} \right] \\\\ &=\dfrac{\dfrac{d}{dx}[x^5] }{\dfrac{d}{dx}[3x+9]} \\\\ &=\dfrac{5x^4}{3} \end{aligned}
Is Wang Fang's work correct? If not, what's her mistake?