derivative of sin(x-1/3 sin^3(x))

解答

\frac{d}{d x} (sin (x) - \frac{1}{3} sin^{3} (x))

cos^{3} (x)

求解步骤

\frac{d}{d x} (sin (x) - \frac{1}{3} sin^{3} (x))

使用微分加减法定则:

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

= \frac{d}{d x} (sin (x)) - \frac{d}{d x} (\frac{1}{3} sin^{3} (x))

\frac{d}{d x} (sin (x)) = cos (x)

\frac{d}{d x} (\frac{1}{3} sin^{3} (x)) = sin^{2} (x) cos (x)

= cos (x) - sin^{2} (x) cos (x)

使用三角恒等式改写

= cos^{3} (x)

\int - 25 sin (5 t - \frac{π}{2}) d t

y^{^{'}} + x e^{y} = 0

\int e^{x} 5 + e^{x} d x

d er i v a t i v e f (x) = 3 x sin (x)

d er i v a t i v e f (x) = \frac{8 x ^{3} - 2 x + 9}{x}