what is the second derivative of f(x) if f(x)=tan^-1 (x)

Question

 differentiation 

Answer 1

The second derivative is the derivative of the derivative of f(x).

 

d/dx(d/dx(f(x))

 

d/dx(d/dx(tan^-1x)) =

 

d/dx(1 / (1 + x²))

 

 

Now take the derivative of  1/(1 + x²)  using quotient rule.