Question

What is the derivative of `sqrt(tan x)`?

Answer 1

`sec^2x/(2sqrttanx)`

Explanation:

The expression can be written as

`(tanx)^(1/2)`

According to the chain rule,

`d/dx[(tanx)^(1/2)]=1/2(tanx)^(-1/2)*d/dx[tanx]`

Since `d/dx[tanx]=sec^2x`,

`d/dx[(tanx)^(1/2)]=sec^2x/(2sqrttanx)`