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### Course: AP®︎/College Calculus AB>Unit 3

Lesson 6: Selecting procedures for calculating derivatives: strategy

# Differentiating functions: Find the error

## Problem

Wang Fang tried to find the derivative of $\frac{{x}^{5}}{3x+9}$. Here is her work:
Step 1: This is the quotient of ${x}^{5}$ and $3x+9$. So we should use the quotient rule.
Step 2:
$\frac{d}{dx}\left[\frac{{x}^{5}}{3x+9}\right]=\frac{\frac{d}{dx}\left[{x}^{5}\right]}{\frac{d}{dx}\left[3x+9\right]}$
Step 3: Finding the derivatives of the factors:
$\begin{array}{rl}\frac{d}{dx}\left[{x}^{5}\right]& =5{x}^{4}\\ \\ \frac{d}{dx}\left[3x+9\right]& =3\end{array}$
Step 4: Putting it all together:
$\begin{array}{rl}& \phantom{=}\frac{d}{dx}\left[\frac{{x}^{5}}{3x+9}\right]\\ \\ & =\frac{\frac{d}{dx}\left[{x}^{5}\right]}{\frac{d}{dx}\left[3x+9\right]}\\ \\ & =\frac{5{x}^{4}}{3}\end{array}$
Is Wang Fang's work correct? If not, what's her mistake?