How do you differentiate #f(x)=(1+cos^2x)^6#?
1 Answer
Apr 7, 2017
Explanation:
differentiate using the
#color(blue)"chain rule"#
#"Given " f(x)=g(h(x))" then"#
#color(red)(bar(ul(|color(white)(2/2)color(black)(f'(x)=g'(h(x))xxh'(x))color(white)(2/2)|)))#
#rArrf'(x)=6(1+cos^2x)^5xxd/dx(1+cos^2x)to(1)#
#"Using the " color(blue)"chain rule " "on " (1+cos^2x)#
#d/dx(1+cos^2x)=2cosxxd/dx(cosx)#
#color(white)(d/dx(1+cos^2x))=-2cosxsinxlarr( -sin2x)#
#"Returning to " (1)#
#f'(x)=-6sin2x(1+cos^2x)^5#
