Question

How do you take the derivative of `y=tan^-1 sqrt(3x)`?

Answer 1

`(dy)/(dx)=sqrt(3x)/(2x(1+3x))`

Explanation:

`y=tan^(-1)sqrt(3x)`

Recall if `y=tan^(-1)x`, then `(dy)/(dx)=1/(1+x^2)`

`(dy)/(dx)=1/(1+(sqrt(3x))^2)times (sqrt3/(2sqrtx))`

`(dy)/(dx)=1/(1+3x)timessqrt(3x)/(2x)`

`(dy)/(dx)=sqrt(3x)/(2x(1+3x))`