What is the differentiation of tan(x/3)?

Answer 1

Answer: 1/3 sec^2 (x/3)

it's a chain rule: d/dx f(g(x)) = g'(x)f'(g(x))

For our function :

g(x) is the inside function = x/3

g'(x) = 1/3

f(x) is the outside function = tan x

f'(x)=sec^2 x

Now put it all together :

d/dx tan(x/3) = 1/3 sec^2(x/3)