Question

How do you differentiate `f(x)= x/(x^3-4 )` using the quotient rule?

Answer 1

Using the quotient rule on `f(x) = (x)/(x^3-4)`, which states that if

`f(x)=` `a(x)` `/` `b(x)`, then `f'(x)=[b(x)*a'(x)-a(x)*b'(x)]/[(b(x))^2]`

Let `b(x) = x^3-4` and `a(x) = x`, so

`f'(x) = [(x^3-4) - (3x^3)]/[(x^3-4)^2]`