设函数y=f(x)由方程e∧y+sin(x+y)=1决定,求二阶导数
来源:学生作业帮 编辑:搜搜考试网作业帮 分类:数学作业 时间:2024/06/17 02:08:49
设函数y=f(x)由方程e∧y+sin(x+y)=1决定,求二阶导数
![设函数y=f(x)由方程e∧y+sin(x+y)=1决定,求二阶导数](/uploads/image/z/3704992-16-2.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0y%3Df%28x%29%E7%94%B1%E6%96%B9%E7%A8%8Be%E2%88%A7y%2Bsin%28x%2By%29%3D1%E5%86%B3%E5%AE%9A%2C%E6%B1%82%E4%BA%8C%E9%98%B6%E5%AF%BC%E6%95%B0)
两边对x求导:
y'e^y+(1+y')cos(x+y)=0,1)
这里可得到y'=-cos(x+y)/[e^y+cos(x+y)]
再对1)求导:
y"e^y+(y')^2e^y+y"cos(x+y)-(1+y')^2 sin(x+y)=0
代入y' 得;
y"(e^y+cos(x+y)]+[cos(x+y)]^2/[e^y+cos(x+y)]^2* e^y-(1-cos(x+y)/(e^y+cos(x+y)))^2sin(x+y)=0
得:y"=-[cos(x+y)]^2/[e^y+cos(x+y)]^2* e^y+(1-cos(x+y)/(e^y+cos(x+y)))^2sin(x+y)}/(e^y+cos(x+y))
y'e^y+(1+y')cos(x+y)=0,1)
这里可得到y'=-cos(x+y)/[e^y+cos(x+y)]
再对1)求导:
y"e^y+(y')^2e^y+y"cos(x+y)-(1+y')^2 sin(x+y)=0
代入y' 得;
y"(e^y+cos(x+y)]+[cos(x+y)]^2/[e^y+cos(x+y)]^2* e^y-(1-cos(x+y)/(e^y+cos(x+y)))^2sin(x+y)=0
得:y"=-[cos(x+y)]^2/[e^y+cos(x+y)]^2* e^y+(1-cos(x+y)/(e^y+cos(x+y)))^2sin(x+y)}/(e^y+cos(x+y))
设函数y=f(x)由方程e∧y+sin(x+y)=1决定,求二阶导数
设函数y=f(x)由方程sin(xy)+e^(x+y)=0确定,求dy/dx
求由隐函数方程y=sin(x+y)所确定的函数y=f(x)的导数
设隐函数y=y(x)由方程x^y-e^y=sin(xy)所确定,求dy
1、设函数y=y(x)由方程e^x-e^y=sin(xy)所确定,求(dy/dx)|x=0;2、设函数f(x)=x^2+
设函数y=f(x)由方程sin y+e^x-xy^2=0确定,求d y/d x
设由方程e的x次方加e的y次方加x乘以y等于1确定函数y=f(x),求y的导数
已知函数y=y(x)是由方程y=sin(x+y)确定,求y的导数
Z=x*sin xy+e^x+y或设y=(x)是由方程xy+sin x+sin y=1确定,求y”
设函数y=f(x)由方程x+y=e^y确定,求dy/dx
求由方程XY=e^x+y确定的隐函数Y的导数Y'
高数导数问题 设y=f(x)由方程xy=e^(x+y)确定,则y``(y的二阶导)等于多少