derivative of tan(5x+1/(2x^2))

解

\frac{d}{d x} (tan (5 x) + \frac{1}{2 x ^{2}})

sec^{2} (5 x) \cdot 5 - \frac{1}{x ^{3}}

解答ステップ

\frac{d}{d x} (tan (5 x) + \frac{1}{2 x ^{2}})

和/差の法則を適用:

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

= \frac{d}{d x} (tan (5 x)) + \frac{d}{d x} (\frac{1}{2 x ^{2}})

\frac{d}{d x} (tan (5 x)) = sec^{2} (5 x) \cdot 5

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

= sec^{2} (5 x) \cdot 5 - \frac{1}{x ^{3}}