How do you differentiate #f(x)=(1+cos^2x)^6#?

1 Answer
Jim G.
Apr 7, 2017

#f'(x)=-6sin2x(1+cos^2x)^5#

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#

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