Question

given: f(x)=x^2+(2)/(x). find f"(x) @Calculus1

Answer 1

use the quotient rule to find the first derivative

Answer 2

\[\large \frac{x^2 +2}{x}\]\[\large \frac{(x)(2x) - (x^2+2)(1)}{x^2}\] Simplify \[\large \frac{x^2 - 2}{x^2}\] This can be simplified more but its easier to leave it in this form to find the second derivative.

Answer 3

Use Quotient Rule again \[\large \frac{(x^2)(2x) - (x^2-2)(2x)}{x^4}\] \[\large \frac{2x^3 - (2x^3 - 4x)}{x^4}\]\[\large \frac{2x^3 - 2x^3 + 4x}{x^4}\]\[\large \frac{4}{x^3}\]

Answer 4

\[\large f \prime \prime (x) = \frac{4}{x^3}\]