已知y=sin(xy),求其导数.

来源：学生作业帮助网编辑：作业帮时间：2024/05/12 01:29:42

已知y=sin(xy),求其导数.
已知y=sin(xy),求其导数.

已知y=sin(xy),求其导数.
解:
由复合函数求导可得:
Y'=COS(XY)*(XY)'
=COS(XY)*(Y+Y'X)
把Y=SIN(XY)代入上式可得:
Y'=(sin(xy)*cos(xy))/(1-x*cos(xy)) .

（1）
两边对x求导：
y'=cos(xy)*(xy)'
=cos(xy)(y+y'x)
=ycos(xy)+xcos(xy)y'
(1-xcos(xy))y'=ycos(xy)
y'=ycos（xy)/(1-xcos(xy))
(2）隐函数求导：
F(x)=y-sin(xy)
f(x)'=-Fx(x,y)/Fy(x,y)
Fx(x,y)=-ycos(xy)
Fy(x,y)=1-xcos(xy)
所以
f(x)'=ycos(xy)/[1-xcos(xy)]

已知y=sin(xy),求其导数. Xy-sin(x+y)=1 求Y的导数已知xy-sin(πy^2)=0 x^2y+siny^2=0求y的一阶导数求函数导数e^x-e^y=sin(xy) x^3+y^3-xy=0,求其隐函数导数? y=sin(a)*cos(a)^2不用导数求其最值已知z=z(x,y)由sin(xy)+z^2=sin(x+z)确定,求z关于x的偏导数已知dx/dy=1/y',试求其三阶导数. 已知函数y=2sin(π/3-2x)求其对称轴方程求其单调增区间 sin（x+y)+e的xy=4求y的导数求 z=sin(xy) 二阶偏导数证明函数f(z)=x^2+2xy-y^2-i(x^2-2xy-y^2)在复平面内处处解析并求其导数证明函数f(z)=x^2+2xy-y^2-i(x^2-2xy-y^2)在复平面内处处解析并求其导数, 求隐函数的导数：sin y+e^x-xy^2=e 计算Z=x^y+sin(xy)的两个一阶偏导数 f(x,y,z)=sin(xy)cos(yz)的二阶偏导数怎么求 f(x,y,z)=sin(xy)cos(yz)的二阶偏导数怎么求求xy-sin(πy^2)=0在（0,-1）的二阶导数. 求xy-sin(πy)=0在（0,1）处的二阶导数