derivative x^2sin^3(x)+xcos^{-3}(x)

解答

导数

x^{2} sin^{3} (x) + x cos^{- 3} (x)

2 x sin^{3} (x) + 3 sin^{2} (x) cos (x) x^{2} + sec^{3} (x) (1 + 3 x tan (x))

求解步骤

\frac{d}{d x} (x^{2} sin^{3} (x) + x cos^{- 3} (x))

使用微分加减法定则:

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

= \frac{d}{d x} (x^{2} sin^{3} (x)) + \frac{d}{d x} (x cos^{- 3} (x))

\frac{d}{d x} (x^{2} sin^{3} (x)) = 2 x sin^{3} (x) + 3 sin^{2} (x) cos (x) x^{2}

\frac{d}{d x} (x cos^{- 3} (x)) = sec^{3} (x) (1 + 3 x tan (x))

= 2 x sin^{3} (x) + 3 sin^{2} (x) cos (x) x^{2} + sec^{3} (x) (1 + 3 x tan (x))