Question

How do you find the derivative of `sqrt(tan x)`?

Answer 1

`(sec^2x)/(2sqrt(tanx)`

Explanation:

differentiate using the `color(blue)"chain rule"`

`d/dx[f(g(x))]=f'(g(x)).g'(x)........ (A)`
`"------------------------------------------"`
Express `sqrttanx=(tanx)^(1/2)`

`f(g(x))=(tanx)^(1/2)rArrf'(g(x))=1/2(tanx)^(-1/2)`

`g(x)=tanxrArrg'(x)=sec^2x`
`"------------------------------------------"`
Substitute these values into (A)

`rArrd/dx(sqrttanx)=1/2(tanx)^(-1/2).sec^2x=sec^2x/(2sqrttanx`