Differentiate the following function with respect to x:x^3e^x - Vidyadip

Question

Differentiate the following function with respect to $\text{x}$:$\text{x}^3\text{e}^\text{x}$

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Answer

Let $\text{u}=\text{x}^3;\text{v}=\text{e}^\text{x}$Then, $\text{u}'=3\text{x}^2;\text{v}'=\text{e}^\text{x}$
Using the product rule:
$\frac{\text{d}}{\text{dx}}(\text{uv})=\text{uv}'+\text{vu}'$
$\frac{\text{d}}{\text{dx}}(\text{x}^3\text{e}^\text{x})=\text{x}^3\text{e}^\text{x}+\text{e}^\text{x}(3\text{x}^2)$
$=\text{x}^2\text{e}^\text{x}(\text{x}+3)$

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