PART 10：例題-根式與分式函數之導函數

設 \(f(x) = \sqrt x  + \frac{1}{{{x^2}}}\) ，試求 \(f'(x)\)

SOL:

\(f(x) = \sqrt x  + \frac{1}{{{x^2}}} = {x^{\frac{1}{2}}} + {x^{ - 2}}\)，

\(f'(x) = \frac{1}{2}{x^{ - \frac{1}{2}}} - 2{x^{ - 3}} = \frac{1}{{2\sqrt x }} - \frac{2}{{{x^3}}}\)