Catherin – Die Kluge Eule https://dieklugeeule.com Sat, 29 Feb 2020 18:50:20 +0000 de-DE hourly 1 https://wordpress.org/?v=6.0.2 https://dieklugeeule.com/wp-content/uploads/2022/04/cropped-logo-smal-2-32x32.jpg Catherin – Die Kluge Eule https://dieklugeeule.com 32 32 Wie unterscheidet man #f (x) = cos ^ 2x #? https://dieklugeeule.com/wie-unterscheidet-man-f-x-cos-2x/ Sat, 29 Feb 2020 18:50:20 +0000 https://dieklugeeule.com/?p=10123 Wie unterscheidet man #f (x) = cos ^ 2x #?

Antworten:

#f'(x)=-sin2x#

Erläuterung:

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#

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