다음 함수의 도함수를 구하라.
$$f(x)=\sqrt[3]{2x-1}- \frac{1}{\sqrt[3]{x^2}}$$
풀이
\(\frac{df}{dx}=\{(2x-1)^{\frac{1}{3}}\}’-\{x^{-\frac{2}{3}}\}’\)
\(=\frac{1}{3}(2x-1)^{-\frac{2}{3}}\cdot(2x-1)’+\frac{2}{3}x^{-\frac{5}{3}}\)
\(=\frac{2}{3}(2x-1)^{-\frac{2}{3}}+\frac{2}{3}x^{-\frac{5}{3}}\)