Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to differentiate the function with respect to x, using the quotient rule, such that:

`f'(x) = ((5x - 1)'(5x + 1) - (5x - 1)(5x + 1)')/((5x + 1)^2)`

`f'(x) = (5(5x + 1) - 5(5x - 1))/((5x + 1)^2)`

Factoring out 5 yields:

`f'(x) = (5(5x + 1 - 5x + 1))/((5x + 1)^2)`

Reducing duplicate members to numerator yields:

`f'(x) = 10/((5x + 1)^2)`

Hence, evaluating the derivative of the given function, using the quotient rule, yields `f'(x) = 10/((5x + 1)^2).`

Unlock This Answer Now