Compute derivative of f(x)= 2 x - Vidyadip

Question

Compute derivative of $f(x)=\sin 2 x$

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Answer

Recall the trigonometric formula sin 2x = 2 sin x cos x. Thus
$\frac{d }{d x}f(x)=\frac{d}{d x}(2 \sin x \cos x)=2 \frac{d}{d x}(\sin x \cos x)$
$=2\left[(\sin x)^{\prime} \cos x+\sin x(\cos x)^{\prime}\right]$
$=2[(\cos x) \cos x+\sin x(-\sin x)]$
$=2\left(\cos ^{2} x-\sin ^{2} x\right)$
= 2cos 2x

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