`f(x) = x^2 + 3x^-3` Find the second derivative of the function.

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to evaluate the first derivative of the function, using the quotient rule for `3x^(-3):`

`f'(x) = 2x - (9x^2)/(x^6)`

You need to simplify by `x^2:`

`f'(x) = 2x - (9)/(x^4)`

You need to evaluate the second derivative of the function, using the first derivative:

`f''(x) = 2 + (36x^3)/(x^8)`

You need to simplify by `x^3:`

`f''(x) = 2 + (36)/(x^5)`

Hence, evaluating the second derivative of the given function, yields `f''(x) = 2 + (36)/(x^5).`