1-cost的求导
@尉莎6610:1 - cost 导数 -
戴殷18935141920…… 显然 dx/dt=a(1-cost) dy/dt=a*sint 那么 dy/dx=sint /(1-cost) 继续求二阶导就得到 d(dy/dx)/dt *dt/dx =[(sint)' *(1-cost) -sint *(1-cost)']/(1-cost)^2 *1/ a(1-cost) =(cost-1)/(1-cost)^2 *1/ a(1-cost) = -1/ [a(1-cost)^2]
@尉莎6610:sint/(1 - cost)求导 -
戴殷18935141920…… f'(t)=[(sint)'(1-cost)-(sint)(1-cost)']/(1-cost)
@尉莎6610:参数方程 x=t - sint y=1 - cost 求二阶导 -
戴殷18935141920…… 先求一阶导 ,一阶导 为 Y对t求导 (sint)比上 X对t求导 (1-cost)结果为(sint)/(1-cost) 求二阶导 的方法与 上面的类似,用一阶导对y求导 比上x对t求导 答案可能是-1/(1-cost)^2
@尉莎6610:参数方程求导 -
戴殷18935141920…… 会步骤不会具体做法,忘记三角函数求导公式了 把1-cost看成一个未知数化简,例如1-cost=m,先对sint求导之后,再对m=1-cost求导,一般式子很麻烦,有很多相同项的都是分步求导,把相同项看成一个未知数
@尉莎6610:sint/(1 - cost)求导 - 作业帮
戴殷18935141920…… [答案] f'(t)=[(sint)'(1-cost)-(sint)(1-cost)']/(1-cost)? =[cost(1-cost)-sintsint]/(1-cost)? =[cost-(cos?t+sin?t)]/(1-cost)? =(cost-1)/(1-cost)? =1/(cost-1)
@尉莎6610:请问刚刚那个题中 y=a(1 - cost)怎么求导的? -
戴殷18935141920…… y^2看作是复合函数,y(x)^2,先对y求导,乘以y对x的导数y^2=2y*y'=2yy'.
@尉莎6610:参数方程x=a(t - sint),y=a(1 - cost)的导数 -
戴殷18935141920…… dx/dt=a(1-cost) dy/dt=asint y'=sint/(1-cost) dy'/dt=[cost(1-cost)-sint*sint]/(1-cost)^2=(cost-1)/(1-cost)^2=-1/(1-cost) y"=(dy'/dt)/(dx/dt)=-1/[a(1-cost)^2]
@尉莎6610:求参数方程x=a(t - sint) y=a(1 - cost)的导数dy/dx的二阶导怎么做? - 作业帮
戴殷18935141920…… [答案] 显然 dx/dt=a(1-cost) dy/dt=a*sint 那么 dy/dx=sint /(1-cost) 继续求二阶导就得到 d(dy/dx)/dt *dt/dx =[(sint)' *(1-cost) -sint *(1-cost)']/(1-cost)^2 *1/ a(1-cost) =(cost-1)/(1-cost)^2 *1/ a(1-cost) = -1/ [a(1-cost)^2]
@尉莎6610:求下列参数方程所确定函数的二阶导数:x=a(t - sint),y=a(1 - cost) - 作业帮
戴殷18935141920…… [答案] dx/dt=a(1-cost)dy/dt=asinty'=sint/(1-cost)dy'/dt=[cost(1-cost)-sint*sint]/(1-cost)^2=(cost-1)/(1-cost)^2=-1/(1-cost)y"=(dy'/dt)/(dx/dt)=-1/[a(1-cost)^2]
@尉莎6610:y=tsint/(1+cost)求导 -
戴殷18935141920…… 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???
戴殷18935141920…… 显然 dx/dt=a(1-cost) dy/dt=a*sint 那么 dy/dx=sint /(1-cost) 继续求二阶导就得到 d(dy/dx)/dt *dt/dx =[(sint)' *(1-cost) -sint *(1-cost)']/(1-cost)^2 *1/ a(1-cost) =(cost-1)/(1-cost)^2 *1/ a(1-cost) = -1/ [a(1-cost)^2]
@尉莎6610:sint/(1 - cost)求导 -
戴殷18935141920…… f'(t)=[(sint)'(1-cost)-(sint)(1-cost)']/(1-cost)
@尉莎6610:参数方程 x=t - sint y=1 - cost 求二阶导 -
戴殷18935141920…… 先求一阶导 ,一阶导 为 Y对t求导 (sint)比上 X对t求导 (1-cost)结果为(sint)/(1-cost) 求二阶导 的方法与 上面的类似,用一阶导对y求导 比上x对t求导 答案可能是-1/(1-cost)^2
@尉莎6610:参数方程求导 -
戴殷18935141920…… 会步骤不会具体做法,忘记三角函数求导公式了 把1-cost看成一个未知数化简,例如1-cost=m,先对sint求导之后,再对m=1-cost求导,一般式子很麻烦,有很多相同项的都是分步求导,把相同项看成一个未知数
@尉莎6610:sint/(1 - cost)求导 - 作业帮
戴殷18935141920…… [答案] f'(t)=[(sint)'(1-cost)-(sint)(1-cost)']/(1-cost)? =[cost(1-cost)-sintsint]/(1-cost)? =[cost-(cos?t+sin?t)]/(1-cost)? =(cost-1)/(1-cost)? =1/(cost-1)
@尉莎6610:请问刚刚那个题中 y=a(1 - cost)怎么求导的? -
戴殷18935141920…… y^2看作是复合函数,y(x)^2,先对y求导,乘以y对x的导数y^2=2y*y'=2yy'.
@尉莎6610:参数方程x=a(t - sint),y=a(1 - cost)的导数 -
戴殷18935141920…… dx/dt=a(1-cost) dy/dt=asint y'=sint/(1-cost) dy'/dt=[cost(1-cost)-sint*sint]/(1-cost)^2=(cost-1)/(1-cost)^2=-1/(1-cost) y"=(dy'/dt)/(dx/dt)=-1/[a(1-cost)^2]
@尉莎6610:求参数方程x=a(t - sint) y=a(1 - cost)的导数dy/dx的二阶导怎么做? - 作业帮
戴殷18935141920…… [答案] 显然 dx/dt=a(1-cost) dy/dt=a*sint 那么 dy/dx=sint /(1-cost) 继续求二阶导就得到 d(dy/dx)/dt *dt/dx =[(sint)' *(1-cost) -sint *(1-cost)']/(1-cost)^2 *1/ a(1-cost) =(cost-1)/(1-cost)^2 *1/ a(1-cost) = -1/ [a(1-cost)^2]
@尉莎6610:求下列参数方程所确定函数的二阶导数:x=a(t - sint),y=a(1 - cost) - 作业帮
戴殷18935141920…… [答案] dx/dt=a(1-cost)dy/dt=asinty'=sint/(1-cost)dy'/dt=[cost(1-cost)-sint*sint]/(1-cost)^2=(cost-1)/(1-cost)^2=-1/(1-cost)y"=(dy'/dt)/(dx/dt)=-1/[a(1-cost)^2]
@尉莎6610:y=tsint/(1+cost)求导 -
戴殷18935141920…… 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???