derivative of x^2sin^4(x+xcos^{-2}(x))

解答

\frac{d}{d x} (x^{2} sin^{4} (x) + x cos^{- 2} (x))

2 x sin^{4} (x) + 4 sin^{3} (x) cos (x) x^{2} + sec^{2} (x) (1 + 2 x tan (x))

求解步骤

\frac{d}{d x} (x^{2} sin^{4} (x) + x cos^{- 2} (x))

使用微分加减法定则:

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

= \frac{d}{d x} (x^{2} sin^{4} (x)) + \frac{d}{d x} (x cos^{- 2} (x))

\frac{d}{d x} (x^{2} sin^{4} (x)) = 2 x sin^{4} (x) + 4 sin^{3} (x) cos (x) x^{2}

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

= 2 x sin^{4} (x) + 4 sin^{3} (x) cos (x) x^{2} + sec^{2} (x) (1 + 2 x tan (x))

y^{^{'}} - 6 y = 2 e^{t}

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (0) = - 4, y^{^{'}} (0) = - 6

x \to + 2 lim ([7 f (x) + g (x)])

y^{^{'}} + e^{t} y = - 17 e^{t}

\int_{0}^{\frac{π}{4}} 5 sec^{2} (x) d x