y=tsint/(1+cost)求导

tsint/(1 + cost)
=[(1 + cost)(tsint)' - tsint(1 + cost)']/(1 + cost)^2
=[(1 + cost)(sint + tcost) + tsintsint]/(1 + cost)^2
=[sint + costsint + tcost + tcostcost + tsintsint]/(1 + cost)^2
=[sint(1 + cost) + t(cost + 1)]/(1 + cost)^2
=(sint + t)(1 + cost)/(1 + cost)^2
=(sint + t)/(1 + cost)

还要化简么???

先化成y=t(1-cost)/sint

分开求，得
y=(1-cost)/sint + t*sint/sint + t(1-cost)*[-cost/(sint)^2]

直接求导就OK了 y'=[(sint+tcost)(1+cost)+t(sint)^2]/(1+cost)^2
=(sint+sint*cost+tcost+t)/(1+cost)^2