derivative x^2sin^6(x)+xcos^{-3}(x)

解答

导数

x^{2} sin^{6} (x) + x cos^{- 3} (x)

2 x sin^{6} (x) + 6 sin^{5} (x) cos (x) x^{2} + sec^{3} (x) (1 + 3 x tan (x))

求解步骤

\frac{d}{d x} (x^{2} sin^{6} (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^{6} (x)) + \frac{d}{d x} (x cos^{- 3} (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^{- 3} (x)) = sec^{3} (x) (1 + 3 x tan (x))

= 2 x sin^{6} (x) + 6 sin^{5} (x) cos (x) x^{2} + sec^{3} (x) (1 + 3 x tan (x))

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

\frac{d}{d y} (\frac{y}{y + \frac{c}{y}})

\int - \frac{7}{x ^{2} + 16} d x

t an g e n t f (x) = \frac{1}{2 x}, at x = 64

\frac{d}{d x} (cos (x + π))