Como você diferencia #f (x) = cos ^ 2x #?

Como voc├¬ diferencia #f (x) = cos ^ 2x #? Responda: #f'(x)=-sin2x# Explica├ž├úo: differentiate using the #color(blue)”chain rule”# #color(orange)”Reminder ” color(red)(bar(ul(|color(white)(2/2)color(black)(dy/dx=(dy)/(du)xx(du)/(dx))color(white)(2/2)|)))# #”Express ” f(x)=cos^2x=(cosx)^2# #”let “u=cosxrArr(du)/(dx)=-sinx# #”then “y=u^2rArr(dy)/(du)=2u# #rArrdy/dx=2u(-sinx)# change u back into terms of x #rArrdy/dx=-2sinxcosx# #color(orange)”Reminder” sin2x=2sinxcosx# #rArrdy/dx=-sin2x#