How do you find the derivative of #y=(1+cos^2x)^6# using the chain rule?
1 Answer
Mar 29, 2016
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 #
