derivative 3/5 cos(2x-pi/4)+pi

解答

导数

\frac{3}{5} cos (2 x - \frac{π}{4}) + π

\frac{3 2 ( cos ( 2 x ) - sin ( 2 x ) )}{5}

求解步骤

\frac{d}{d x} (\frac{3}{5} cos (2 x - \frac{π}{4}) + π)

化简

\frac{3}{5} cos (2 x - \frac{π}{4}) + π : \frac{3 ( 2 cos ( 2 x ) + 2 sin ( 2 x ) )}{10} + π

= \frac{d}{d x} (\frac{3 ( 2 cos ( 2 x ) + 2 sin ( 2 x ) )}{10} + π)

使用微分加减法定则:

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

= \frac{d}{d x} (\frac{3 ( 2 cos ( 2 x ) + 2 sin ( 2 x ) )}{10}) + \frac{d π}{d x}

\frac{d}{d x} (\frac{3 ( 2 cos ( 2 x ) + 2 sin ( 2 x ) )}{10}) = \frac{3 2 ( cos ( 2 x ) - sin ( 2 x ) )}{5}

\frac{d π}{d x} = 0

= \frac{3 2 ( cos ( 2 x ) - sin ( 2 x ) )}{5} + 0

化简

= \frac{3 2 ( cos ( 2 x ) - sin ( 2 x ) )}{5}

a re a x^{2} e^{- x}, x e^{- x}

in v erse l a pl a ce \frac{2 s}{s ^{2} + 9}

y^{^{'}} = 2 - (\frac{x}{20})

a re a y = 2 x, y = \frac{x}{2}

x \to - 6 lim (\frac{x ^{2} + 8}{x + 6})