Question

How do you differentiate `y=(arctan(x))^(1/2)`?

Answer 1

`dy/dx=1/(2(1+x^2)(arctanx)^(1/2)`

Explanation:

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

`"given "y=f(g(x))" then"`

`dy/dx=f'(g(x))xxg'(x)larr"chain rule"`

`rArrdy/dx=1/2(arctanx)^(-1/2)xxd/dx(arctanx)`

`color(white)(rArrdy/dx)=1/2(arctanx)^(-1/2)xx1/(1+x^2)`

`color(white)(rArrdy/dx)=1/(2(1+x^2)(arctanx)^(1/2))`