How do you find the derivative of #y=(1+cos^2x)^6# using the chain rule?

1 Answer
Mar 29, 2016

Answer:

#dy/dx = -6sin2x (1 + cos^2 x)^5 #

Explanation:

Differentiate using the#color(blue)" chain rule " #

#d/dx [ f(g(x)) ] = f'(g(x)) . g'(x) #

here : f(g(x)) = #(1 + cos^2 x)^6 #

#rArr f'(g(x)) = 6(1 + cos^2 x)^5 #
#"-----------------------------------------------------"#

and g(x) =#(1 + cos^2 x) → g'(x) = 2cosx .d/dx(cosx) #

= 2cosx.(-sinx) = - 2sinxcosx = - sin2x
#"------------------------------------------------------"#

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

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