两边同时取自然对数，即有
y=lnxy
两边求导，得
dy/dx
=1/xy*(y+x*dy/dx)
dy/dx
=y/x(1-y)
所以
d^2y/dx^2
=y(2-y)/[x^2(1-y)^3]
求由参数方程确立的二阶导数d^2*y\/dx^2
y=lnxy 两边求导，得 dy\/dx =1\/xy*(y+x*dy\/dx)dy\/dx =y\/x(1-y)所以 d^2y\/dx^2 =y(2-y)\/[x^2(1-y)^3]
求由参数方程确立的二阶导数d^2*y\/dx^2
dx\/dt=-2[1\/(1+t^2)],dy\/dt=t^2-1则y'=dy\/dx=(dy\/dt)\/(dx\/dt)=[t^2-1]\/{-2[1\/(1+t^2)]}=(1\/2)(1-t^4)则dy'\/dt=-2t^3 y"=dy'\/dx=(dy'\/dt)\/(dx\/dt)=(-2t^3)\/{-2[1\/(1+t^2)]}=t^3(1+t^2)...
求下列参数方程的二阶导数d^2y\/dx^2
==>d(dy\/dx)=dt ∴d²y\/dx²=y''=d(dy\/dx)\/dx =dt\/[f''(t)dt]=1\/f''(t)。
关于参数方程的二阶导数
设y=f(t) x=g(t)d^2y\/dx^2=d(dy\/dx)\/dx =d[f'(t)\/g'(t)]\/dx =d[f'(t)\/g'(t)]\/dt*(dt\/dx)=d[f'(t)\/g'(t)]\/dt*[1\/(dx\/dt)]=[f''(t)g'(t)-f'(t)g''(t)]\/[g'(t)]^2*[1\/g'(t)]=[f''(t)g'(t)-f'(t)g''(t)]\/[g'(t)]^3...
急!求下列参数方程所确定的函数y的二阶导数d^2y\/dx^2
dt\/dx)]\/dt * dt\/dx =d[(3-3t^2)\/(2-2t)]\/dt * 1\/(2-2t)=3\/[4(1-t)]2 dy\/dt=tf''(t);dx\/dt=f''(t);dt\/dx=1\/f''(t)d^2y\/dx^2=d(dy\/dx))\/dx =[d(dy\/dt * dt\/dx)]\/dt * dt\/dx =d[(tf''(t))\/f''(t)]\/dt * 1\/f''(t)=1\/f''(t)
求参数方程所确定的函数的二阶导数d^2y\/dx^2
不够明白，是这样吗：
由参数方程所确定的函数的二次导数的推导过程,请详细啊!谢谢。_百度知 ...
x=x(t)y=y(t)dx\/dt=x'(t)dy\/dt=y'(t)y'(x)=dy\/dx=dy\/dt \/(dx\/dt)=y'(t)\/x'(t)y"(x)=d^2y\/dx^2=d(y'(x))\/dx=d(y'(x))\/dt \/(dx\/dt)=d(y'(t)\/x'(t))\/dt \/x'(t)=[y"(t)x'(t)-y'(t)x"(t)])\/[x'(t)]^3 ...
求下列参数方程所确定的函数的二阶导数(d^2y)\/(dx^2):
y'=0.5*2\/√(2x)=1\/√(2x)y'√(2x)=1 y''√(2x)+y' [0.5*2\/√(2x)]=0 y'' = -1\/(2x)2. x=acost y=bsint y'=dy\/dx=-(b\/a)cost\/sint=-(b\/a)(x\/a)\/(y\/b)=-b^2x\/(a^2y) (1)x^2\/a^2+y^2\/b^2=1 y=b√[(1-x^2\/a^2)] ...
数学参数方程二阶导数公式
这里因为d^2y\/dx^2=d(y')\/dx, 这里y'=dy\/dx=g(t)而因为是参数方程,都要化成对t的求导才行。所以上式分子分母同时除以dt, 化为:[d(y')\/dt]\/(dx\/dt) 这就是分母里有这个一阶导数的原因。 追问 我明白要化成对t的求导,二阶导数不就是在对一阶导数求导吗,问题是前面已经对一阶导数求导了,我不...
...y=b sin t 求参数方程所确定的函数的二介导数(d^2y)\/(dx^2)怎么...
首先 （d^2y）\/（dx^2）=d（dy\/dx）\/（dx）而 dy\/dx=（dy\/dt ） · dt\/dx）=（dy\/dt ）\/（dx\/dt ）=b cost*[-1\/（asint）]= -b\/a cot t 所以 d（dy\/dx）\/（dx）=[d（dy\/dx）\/dt ] · （dt\/dx）=[d（dy\/dx）\/dt ] \/（dx\/dt）=b\/a*（1\/sinx^...
