How do you differentiate $sinxcosx$ ?

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Answer 1 · 2017-03-09T16:54:24

$d/dx sinxcosx = cos2x$

Method 1 - Manipulation

$d/dx sinxcosx = d/dx 1/2 sin 2x$
$" " = 1/2 d/dx sin 2x$
$" " = 1/2 2cos2x$
$" " = cos2x$

Method 2: Product Rule

$d/dx sinxcosx = (sinx)(d/dxcosx)+(d/dxsinx)(cosx)$
$" " = (sinx)(-sinx)+(cosx)(cosx)$
$" " = cos^2x-sin^2x$
$" " = cos2x$

How do you differentiate sinxcosxsinxcosx?