Differentiate the following function with respect to x:(2x^2-3) - Vidyadip

Question

Differentiate the following function with respect to x:$(\text{2x}^2-3)\sin\text{x}$

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Answer

Let $\text{u}=\text{2x}^2-3;\text{v}=\sin\text{x}$Then, $\text{u}'=\text{4x};\text{v}'=\cos\text{x}$
Using the product rule:
$\frac{\text{d}}{\text{dx}}(\text{uv})=\text{uv}'+\text{vu}'$
$\frac{\text{d}}{\text{dx}}[(\text{2x}^2-3)\sin\text{x}]=(\text{2x}^2-3)\cos\text{x}+\text{4x}\sin\text{x}$

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