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

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#