derivative 12sqrt(x)+16x^{3/4}

解

導関数

12 x + 16 x^{\frac{3}{4}}

\frac{6}{x ^{\frac{1}{2}}} + \frac{12}{x ^{\frac{1}{4}}}

解答ステップ

\frac{d}{d x} (12 x + 16 x^{\frac{3}{4}})

和/差の法則を適用:

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

= \frac{d}{d x} (12 x) + \frac{d}{d x} (16 x^{\frac{3}{4}})

\frac{d}{d x} (12 x) = \frac{6}{x ^{\frac{1}{2}}}

\frac{d}{d x} (16 x^{\frac{3}{4}}) = \frac{12}{x ^{\frac{1}{4}}}

= \frac{6}{x ^{\frac{1}{2}}} + \frac{12}{x ^{\frac{1}{4}}}