How to do this derivative?

Question

f(x)= (x^2-1) / (x^2+1) Please show me steps. Im stuck on it.

Answer 1

f(x) = (x² - 1) / (x² + 1)

 

I suggest using the quotient rule:

 

(u/v)' = (u'v - uv') / v²

 

u = x² - 1

v = x² + 1

 

f'(x) = [2x(x² + 1) - (x² - 1)(2x)] / (x² + 1)²

 

You can simplify it from here.

 

f'(x) = 2x(x² + 1 - x² + 1) / (x² + 1)²

 

f'(x) = 2x(2) / (x² + 1)²

 

f'(x) = 4x / (x² + 1)²