# How do you differentiate f(x)=-cosx*(-2sinx) using the product rule?

Feb 12, 2017

So $\frac{\mathrm{dy}}{\mathrm{dx}} - \cos \left(x\right) \cdot - 2 \sin \left(x\right) = \left(- \cos \left(x\right)\right) ' \left(- 2 \sin \left(x\right)\right) + \left(- \cos \left(x\right)\right) \left(- 2 \sin \left(x\right)\right)$
$= \sin \left(x\right) \cdot \left(- 2 \sin \left(x\right)\right) + \left(- \cos \left(x\right)\right) \left(- 2 \cos \left(x\right)\right)$
$= - 2 {\sin}^{2} \left(x\right) + 2 {\cos}^{2} \left(x\right)$