Question

What is the derivative of `y= arctan (sqrt 3x^2 -1)`?

Answer 1

`y'=(2sqrt3x)/(1+(sqrt3x^2+1)^2)`

Explanation:

`color(blue)(d/dx)tan^-1u=((du)/dx)/(1+u^2)`

Let `u=sqrt3x^2-1` , `(du)/dx=2sqrt3x`

`y'=(2sqrt3x)/(1+(sqrt3x^2+1)^2)`