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

Question

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

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Answer

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

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