# How do you use the Product Rule to find the derivative of f(x)=cot(x)cos(x)?

$- \cos x - \cot x \cos e c x$
let $u \left(x\right) = \cot x$$v \left(x\right) = \cos x$$, f \left(x\right) = u \left(x\right) v \left(x\right)$
according to product rule$d \frac{u v}{\mathrm{dx}} = u \frac{\mathrm{dv}}{\mathrm{dx}} + v \frac{\mathrm{du}}{\mathrm{dx}}$
d(cotxcossx)/dx=cotx(dcosx/dx)+cosx(d/dx(cotx)) =cotx(-sinx)+cosx(-cosec^2x)=-cosx-cotxcosecx