Differentiate the following function with respect to x: - Vidyadip

Question

Differentiate the following function with respect to x:
$\sin\text{x}\cos\text{x}$

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Answer

Let $\text{u}=\sin\text{x};\text{v}=\cos\text{x}$Then, $\text{u}'=\cos\text{x};\text{v}'=-\sin\text{x}$
Using the product rule:
$\frac{\text{d}}{\text{dx}}(\text{uv})=\text{uv}'+\text{vu}'$
$\frac{\text{d}}{\text{dx}}(\sin\text{x}\cos\text{x})=\sin\text{x}(-\sin\text{x})+\cos\text{x}.\cos\text{x}$
$=-\sin^2\text{x}+\cos^2\text{x}$
$=\cos2\text{x}$

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