Differentiate from first principles. (tan x)^1/2

Question

Differentiate from first principles. 

(tan x)^1/2

Answer 1

The answer actually is

 

y ' = 1/2sec^2(x)/(sqrt(tanx))

Ken forgot to subtract 1 from the power therefore leaving tanx to the -1/2 power I wrote the -1/2 power in the denominator as a positive 1/2 power

Answer 2

Use power rule and chain rule (avoid the first principle of doing it by the limit of a 'Newton auotient').

 

y = (tan x)^½

 

y' = ½•tan x•sec²x