d^2y/dx^2=[d(dy/dx)/dt]/dx/dt
=1/4*(-1/2)*(1+t^2)^(-3/2)/(4t)
=-1/32*(1+t^2)^(-3/2)/t
急急急急设x=2t^(2)-1,y=根号(1+t^2).求dy\/dx和d^2y\/dx^2
d^2y\/dx^2=[d(dy\/dx)\/dt]\/dx\/dt =1\/4*(-1\/2)*(1+t^2)^(-3\/2)\/(4t)=-1\/32*(1+t^2)^(-3\/2)\/t
已知参数方程x=e^(2t)-1,y=2e^t,求dy\/dx,d^2y\/dx^2
是对y求导，y\/2=e^t,化简得y^2=4x+4,两边对x求导，2y乘dy\/dx=4x+4 (1)，dy\/dx=(2x+2)\/y (2),对（1）两边对x继续求导，得2dy\/dx+2y*(d^2y\/dx^2)=4 (3),化简得y''=(2-y')\/y
设{x=2t^3+2 y=e^2t-1 ,求dy\/dx,d^2y\/dx^2
利用复合函数求导法.dy\/dx=(dy\/dt)\/(dx\/dt)=2e^(2t)\/(6t^2)=e^(2t)\/(3t^2)故d^2y\/dx^2=d(dy\/dx)\/dx=[d(dy\/dx)\/dt]\/(dx\/dt)=d[e^(2t)\/(3t^2)]\/dt*1\/(6t^2)=[2e^(2t)*3t^2-e^(2t)*6t]\/(6t^2)=e^(2t)*(t-1)\/t ...
...√(1+t^2),y=arctant, 求 dy\/dx及d^2·y\/d·x^2 有详细过程最好 谢...
这是参数方程求导 x'=t\/（1+t^2)y'=1\/（1+t^2)x''= [（1+t^2)-t*2t]\/（1+t^2)^2=（1-t^2)\/（1+t^2)^2 y''=-2t\/（1+t^2)^2 dy\/dx=y'\/x'=1\/t d^2y\/dx^2=(x'y''-x''y')\/(x')^3 =[-2t^2\/（1+t^2)^3-(1-t^2)\/（1+t^2)^3]\/[t\/...
已知参数方程x=2t-t^2 y=3t-t^3,求d^2y\/dx^2
对于参数方程：y=y(t)=3t-t^3x=x(t)=2t-t^2一阶导数：dy\/dx=(dy\/dt)\/(dx\/dt)=y'\/x'=3(1-t^2) \/ 2(1-t) =3(1+t)\/2那么,一阶微分：dy=3(1+t)\/2 dx二阶导数：d^2\/dx^2=d(dy\/dx)\/dx=d(y'\/x')\/dx=[d(y'\/x')\/dt] \/ [dx\/dt]...
x=2t^2,y=e^t+e^2,求d^2y\/dx^2,请写出具体步骤, 即求Y对X的二阶导数
d^2y\/dx^2=(d^2y\/dt)\/(dx^2\/dt)=e^t\/16t^3
...参数方程x=ln√(1+t^2) y=arctant所确定的函数的导数求d^2y\/dx^2
答：x=ln√(1+t^2)，dx\/dt=[1\/√(1+t^2)]*(1\/2)*2t\/√(1+t^2)=t\/(1+t^2)y=arctant，dy\/dt=1\/(1+t^2)所以：dy\/dx=1\/t y''=d²y\/dx²=d(dy\/dx)\/dx=[d(1\/t)\/dt]\/(dx\/dt)=(-1\/t^2)\/[t\/(1+t^2)]=-(1+t^2)\/t^3 所以：dy\/dx=1...
...大括号”x=arctan2t,y=t+ln(1+4t^2)求dy\/dx和dy^2\/dx^2_百度知 ...
dy\/dx=(dy\/dt)\/(dx\/dt)dy\/dt=1+[8t\/(1+4t^2)]=[(1+2t)^2]\/(1+4t^2)dx\/dt=1\/(1+4t^2)所以dy\/dx=(1+2t)^2 [d(dy\/dx)]\/dt=4(1+2t)dy^2\/dx^2=[d(dy\/dx)]\/dx={[d(dy\/dx)]\/dt}\/(dx\/dt)=4((1+2t)(1+4t^2)所以dy^2\/dx^2=4((1+2t)(1+4t...
求导数的相关题 x=ln(1+t^2) y=arctant 求d^2 y\/dx^2=
-(t^2+1)\/(4t^3)dy\/dt=1\/(t*t+1)dx\/dt=2t\/(t*t+1)dy\/dx=1\/2t d^2 y\/dx^2=[d(1\/2t)\/dt]*(t*t+1)\/2t=-(t^2+1)\/(4t^3)
高等数学第二章习题 设方程组 x=2t-1, te^y+y+1=0 确定y是x的函数...
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