Question

How do you differentiate `f(x)=x/(x+c/x)`?

Answer 1

Start by simplifying the entire expression.

`f(x) = x/((x^2 + c)/x)`

`f(x) = x^2/(x^2 + c)`

`f'(x) = (2x(x^2 + c) - 2x(x^2))/(x^2 + c)^2`

`f'(x) = (2x^3 + 2xc - 2x^3)/(x^2 + c)^2`

`f'(x) = (2xc)/(x^2 + c)^2`

Hopefully this helps!