Question

Question #1abd1

Answer 1

`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.