derivative of x^2sin^8(x+xcos^{-6}(x))

解

\frac{d}{d x} (x^{2} sin^{8} (x) + x cos^{- 6} (x))

2 x sin^{8} (x) + 8 sin^{7} (x) cos (x) x^{2} + sec^{6} (x) + \frac{6 x sin ( x )}{cos ^{7} ( x )}

解答ステップ

\frac{d}{d x} (x^{2} sin^{8} (x) + x cos^{- 6} (x))

和/差の法則を適用:

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

= \frac{d}{d x} (x^{2} sin^{8} (x)) + \frac{d}{d x} (x cos^{- 6} (x))

\frac{d}{d x} (x^{2} sin^{8} (x)) = 2 x sin^{8} (x) + 8 sin^{7} (x) cos (x) x^{2}

\frac{d}{d x} (x cos^{- 6} (x)) = sec^{6} (x) + \frac{6 x sin ( x )}{cos ^{7} ( x )}

= 2 x sin^{8} (x) + 8 sin^{7} (x) cos (x) x^{2} + sec^{6} (x) + \frac{6 x sin ( x )}{cos ^{7} ( x )}