# Which of the following is the derivative with respect to x of (x + 1)^3 - x^3?

Date of Exam

Subject

**Problem**

Which of the following is the derivative with respect to *x* of $(x + 1)^3 - x^3$?

A. 6x + 3 |
C. 1 + 2x - 3x^{2} |

B. 3x^{2} + 2x + 1 |
D. 6x - 3 |

**Answer Key**

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[ A ]

**Solution**

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$\begin{align}

\dfrac{d}{dx} \Big[ (x + 1)^3 - x^3 \Big] & = 3(x + 1)^2 - 3x^2 \\

& = 3(x^2 + 2x + 1) - 3x^2 \\

& = 3x^2 + 6x + 3 - 3x^2 \\

& = 6x + 3 ~ \leftarrow ~ \text{answer}

\end{align}$

\dfrac{d}{dx} \Big[ (x + 1)^3 - x^3 \Big] & = 3(x + 1)^2 - 3x^2 \\

& = 3(x^2 + 2x + 1) - 3x^2 \\

& = 3x^2 + 6x + 3 - 3x^2 \\

& = 6x + 3 ~ \leftarrow ~ \text{answer}

\end{align}$

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