Question #1abd1

1 Answer
Apr 16, 2017

#6[tan(2x)]^2sec^2(2x)#

Explanation:

Let #f(x)=tan^3(2x)#.

By rewriting a bit so that the order of composition is clearer,

#Rightarrow f(x)=[tan(2x)]^3#

By Power Rule & Chain Rule,

#Rightarrow f'(x)=3[tan(2x)]^2cdot[tan(2x)]'#

By #(tan x)'=sec^2x# & Chain Rule,

#=3[tan(2x)]^2cdot sec^2(2x)cdot(2x)'#

By Power Rule,

#=3[tan(2x)]^2cdot sec^2(2x)cdot2#

By cleaning upa bit,

#=6[tan(2x)]^2sec^2(2x)#

I hope that this was clear.