已知x=t(1-cost),y=tcost,确定了y=f(x),求dy/dx和d^2y/dx^2,

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已知x=t(1-cost),y=tcost,确定了y=f(x),求dy/dx和d²y/dx²
y'=dy/dx=(dy/dt)/(dx/dt)=(cost-tsint)/(1-cost+tsint)；
y''=d²y/dx²=dy'/dx=(dy'/dt)/(dx/dt)
={[(1-cost+tsint)(-sint-sint-tcost)-(cost-tsint)(sint+sint+tcost)]/(1-cost+tsint)²}/(1-cost+tsint)
=[(1-cost+tsint)(-2sint-tcost)-(cost-tsint)(2sint+tcost)]/(1-cost+tsint)³
=[-(1-cost+tsint)(2sint+tcost)-(cost-tsint)(2sint+tcost)]/(1-cost+tsint)³
=[(2sint+tcost)(1+cost-tsint-cost+tsint)]/(1-cost+tsint)³
=(2sint+tcost)/(1-cost+tsint)³
再问：倒数第二行，第二个括号的1是不是应该为-1，因为倒数第三行的1前面有负号的~所以结果是不是也得加负号啊
再答：你说的对！你很细心！我疏忽了！修正如下：倒数第二行开始： =[(2sint+tcost)(-1+cost-tsint-cost+tsint)]/(1-cost+tsint)³ =-(2sint+tcost)/(1-cost+tsint)³

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