How do you differentiate #f(x)=(tan^2 3x)^(7/3)# using the chain rule?
1 Answer
Apr 5, 2016
Explanation:
differentiate using the
#color(blue)" chain rule " #
#d/dx [f(g(x)) ] = f'(g(x)) . g'(x) #
#"------------------------------------------------------------------------"# f(g(x)) =
#(tan^2 3x)^(7/3)rArr f'(g(x)) = 7/3(tan^2 3x)^(4/3) # g(x) =
#tan^2 3x rArr g'(x) = 2tan3x . d/dx(tan3x) #
#d/dx(tan3x) = sec^2 3x .d/dx(3x) = 3sec^2 3x #
#"-----------------------------------------------------------------------"# Now combining these results together
f'(x) =
#7/3(tan^2 3x)^(4/3).2tan3x.3sec^2 3x #
# = 42/3(tan^2 3x)^(4/3) tan3x sec^2 3x #
