Como você diferencia #f (x) = cos ^ 2x #?
Responda:
#f'(x)=-sin2x#
Explicação:
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#