d/(dt)((s)(1/(9pi)cos(9t)-1/(3pi)sin(3t)))

解答

\frac{d}{d t} ((s) (\frac{1}{9 π} cos (9 t) - \frac{1}{3 π} sin (3 t)))

s (- \frac{1}{π} sin (9 t) - \frac{1}{π} cos (3 t))

求解步骤

\frac{d}{d t} ((s) (\frac{1}{9 π} cos (9 t) - \frac{1}{3 π} sin (3 t)))

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= s \frac{d}{d t} (\frac{1}{9 π} cos (9 t) - \frac{1}{3 π} sin (3 t))

使用微分加减法定则:

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

= s (\frac{d}{d t} (\frac{1}{9 π} cos (9 t)) - \frac{d}{d t} (\frac{1}{3 π} sin (3 t)))

\frac{d}{d t} (\frac{1}{9 π} cos (9 t)) = - \frac{1}{π} sin (9 t)

\frac{d}{d t} (\frac{1}{3 π} sin (3 t)) = \frac{1}{π} cos (3 t)

= s (- \frac{1}{π} sin (9 t) - \frac{1}{π} cos (3 t))

e x p an d \frac{9 x ^{2} + 4}{5 ( 3 x ^{3} + 4 x ) ^{\frac{4}{5}}}

e x p an d \frac{x ( x + y + z )}{z ( x - y + z )}

e x p an d (\frac{63}{32})^{2}

e x p an d \frac{- 4 x ^{2} + 4 x + 4}{( x ^{2} + 1 ) ^{2}}

e x p an d 3098.5 (x + y - 0.1)^{2}