# How do you differentiate f(x)=sinxcosx using the product rule?

Jan 8, 2016

$f ' \left(x\right) = {\cos}^{2} x - {\sin}^{2} x$ or $1 - 2 {\sin}^{2} x$
The product rule states that if $f \left(x\right) = g \left(x\right) h \left(x\right)$ then $f ' \left(x\right) = g \left(x\right) h ' \left(x\right) + g ' \left(x\right) h \left(x\right)$
$f \left(x\right) = \sin x \cos x$
$\therefore f ' \left(x\right) = \sin x \left(- \sin x\right) + \cos x \cos x$