derivative y=x^2sin^6(x)+xcos^{-2}(x)

解

導関数

y = x^{2} sin^{6} (x) + x cos^{- 2} (x)

2 x sin^{6} (x) + 6 sin^{5} (x) cos (x) x^{2} + sec^{2} (x) (1 + 2 x tan (x))

解答ステップ

\frac{d}{d x} (x^{2} sin^{6} (x) + x cos^{- 2} (x))

和/差の法則を適用:

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

= \frac{d}{d x} (x^{2} sin^{6} (x)) + \frac{d}{d x} (x cos^{- 2} (x))

\frac{d}{d x} (x^{2} sin^{6} (x)) = 2 x sin^{6} (x) + 6 sin^{5} (x) cos (x) x^{2}

\frac{d}{d x} (x cos^{- 2} (x)) = sec^{2} (x) (1 + 2 x tan (x))

= 2 x sin^{6} (x) + 6 sin^{5} (x) cos (x) x^{2} + sec^{2} (x) (1 + 2 x tan (x))