Question

What is the derivative of `arctan(x)^(1/2)`?

Answer 1

`f'(x)=(1)/(2sqrt(x)(1+x)`

Explanation:

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

Using the chain rule:

`f'(x)=(1)/(1+x)xx1/2x^(-1/2)`

`f'(x)=(x^(-1/2))/(2(1+x))`

`f'(x)=(1)/(2sqrt(x)(1+x)`