Question
Differentiate the following functions by the product rule and the other method and verify that the answer from both the methods is the same.
$(\text{x}+2)(\text{x}+3)$
✓
Answer
Let $\text{u}=(\text{x}+2);\text{v}=(\text{x}+3)$
Then,
$\text{u}'=1;\text{v}'=1$Using the product rule:
$\frac{\text{d}}{\text{dx}}(\text{uv})=\text{uv}'+\text{vu}'$
$\frac{\text{d}}{\text{dx}}[(\text{x}+2)(\text{x}+3)]=(\text{x}+2)1+(\text{x}+3)1$
$=\text{x}+2+\text{x}+3$
$=\text{2x}+5$
Alternate method
$\frac{\text{d}}{\text{dx}}[(\text{x}+2)(\text{x}+3)]$
$=\frac{\text{d}}{\text{dx}}(\text{x}^2+\text{5x}+6)$
$=\text{2x}+5$
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