derivative \sqrt[3]{x^2}+sqrt(x)

解

derivative

\frac{2 x}{3 ( x ^{2} ) ^{\frac{2}{3}}} + \frac{1}{2 x}

解答ステップ

\frac{d}{d x} (3 x^{2} + x)

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (3 x^{2}) + \frac{d}{d x} (x)

\frac{d}{d x} (3 x^{2}) = \frac{2 x}{3 ( x ^{2} ) ^{\frac{2}{3}}}

\frac{d}{d x} (x) = \frac{1}{2 x}

= \frac{2 x}{3 ( x ^{2} ) ^{\frac{2}{3}}} + \frac{1}{2 x}