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AP®︎ Calculus AB (2017 edition)

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

Lesson 1: Basic differentiation rules

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Basic derivative rules: find the error

AP.CALC: FUN‑3 (EU), FUN‑3.A (LO), FUN‑3.A.2 (EK)

Google Classroom

Emma tried to find the derivative of 1, plus, 6, x using basic differentiation rules. Here is her work:

\begin{aligned} &&&\phantom{=}\dfrac{d}{dx}(1+6x) \\\\ \text{Step 1} &&&=\dfrac{d}{dx}(1)+\dfrac{d}{dx}(6x) \\\\ \text{Step 2} &&&=1+\dfrac{d}{dx}(6x) \\\\ \text{Step 3} &&&=1+6\dfrac{d}{dx}(x) \\\\ \text{Step 4} &&&=1+6\cdot 1 \\\\ \text{Step 5} &&&=7 \end{aligned}

At which step did Emma make a mistake, if at all?

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