derivative f(x)= 4/(3x^2)+1/(x^{2.1)}

解

導関数

f (x) = \frac{4}{3 x ^{2}} + \frac{1}{x ^{2.1}}

- \frac{2.66666 \dots}{x ^{3}} - \frac{2.1}{x ^{3.1}}

解答ステップ

\frac{d}{d x} (\frac{4}{3 x ^{2}} + \frac{1}{x ^{2.1}})

簡素化

\frac{4}{3 x ^{2}} + \frac{1}{x ^{2.1}} : \frac{1.33333 \dots}{x ^{2}} + \frac{1}{x ^{2.1}}

= \frac{d}{d x} (\frac{1.33333 \dots}{x ^{2}} + \frac{1}{x ^{2.1}})

和/差の法則を適用:

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

= \frac{d}{d x} (\frac{1.33333 \dots}{x ^{2}}) + \frac{d}{d x} (\frac{1}{x ^{2.1}})

\frac{d}{d x} (\frac{1.33333 \dots}{x ^{2}}) = - \frac{2.66666 \dots}{x ^{3}}

\frac{d}{d x} (\frac{1}{x ^{2.1}}) = - \frac{2.1}{x ^{3.1}}

= - \frac{2.66666 \dots}{x ^{3}} - \frac{2.1}{x ^{3.1}}