Question

What is the derivative of `Arctan(sqrt(5x))`?

Answer 1

the answer
`d/dx[Arctan(sqrt(5x))]=[5/(2sqrt5x)]/[1+5x]=sqrt(5)/(2sqrt(x)*(5x+1))`

Explanation:

note that

`d/dx[arctan(u)]=((du)/dx)/[1+u^2]`

now let's derive `Arctan(sqrt(5x))`

`d/dx[Arctan(sqrt(5x))]=[5/(2sqrt5x)]/[1+5x]=sqrt(5)/(2*sqrt(x)*(5*x+1))`