derivative f(x)=139+(36)/x+(x^2)/(16)

解

導関数

f (x) = 139 + \frac{36}{x} + \frac{x ^{2}}{16}

\frac{x}{8} - \frac{36}{x ^{2}}

解答ステップ

\frac{d}{d x} (139 + \frac{36}{x} + \frac{x ^{2}}{16})

和/差の法則を適用:

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

= \frac{d}{d x} (139) + \frac{d}{d x} (\frac{36}{x}) + \frac{d}{d x} (\frac{x ^{2}}{16})

\frac{d}{d x} (139) = 0

\frac{d}{d x} (\frac{36}{x}) = - \frac{36}{x ^{2}}

\frac{d}{d x} (\frac{x ^{2}}{16}) = \frac{x}{8}

= 0 - \frac{36}{x ^{2}} + \frac{x}{8}

簡素化

= \frac{x}{8} - \frac{36}{x ^{2}}