Question

What is the derivative of `sqrttan x`?

Answer 1

`f'(x)=1/(2sec^2x)`

Explanation:

Original Equation:
`f(x)=sqrt(tanx)`

Rearrange:
`tanx^(1/2)`

Use Chain Rule to derive:
`(1/2)(sec^2x)(tanx)^(-1/2)`

Rearrange to make exponents positive:
`(sec^2x)/(2(tanx)^(1/2)`

Your final answer should be:
`f'(x)=(sec^2x)/(2sqrttanx`

Answer 2

`sec^2x/(2sqrttanx`

Explanation:

First rewrite the function:

`f(x)=(tanx)^(1/2)`

According to the chain rule,

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

so,

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

`=>1/(2sqrttanx)*sec^2x`

`=>sec^2x/(2sqrttanx`