Question

How do you differentiate `f(t)=root3(1+tant)`?

Answer 1

`f'(t) = sec^2t/(3(1+tant)^(2/3))`

Explanation:

`f(t) = root3(1+tant)`

`= (1+tant)^(1/3)`

`f'(t) = 1/3(1+tant)^(-2/3) * d/dt(1+tant)` [Power rule and Chain rule]

`= 1/3(1+tant)^(-2/3) * (0+ sec^2t)` [Standard differential]

`=sec^2t/(3(1+tant)^(2/3))`