设函数y=f(x)由方程sin(x^2+y)=xy 确定,求dy\dx
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/08 12:40:06
设函数y=f(x)由方程sin(x^2+y)=xy 确定,求dy\dx
这个题目要利用隐函数的求导法则.
则sin(x^2+y)=xy (两边同时求导,还要结合复合函数的求导法则)
cos(x^2+ y)*(2x+y′)=y+xy′
2xcos(x^2+y)-y=xy′-y′ cos(x^2+ y)
2xcos(x^2+y)-y=y′(x-cos(x^2+ y))
y′={2xcos(x^2+y)-y}/(x-cos(x^2+ y))
则dy\dx= y′={2xcos(x^2+y)-y}/(x-cos(x^2+ y))
则sin(x^2+y)=xy (两边同时求导,还要结合复合函数的求导法则)
cos(x^2+ y)*(2x+y′)=y+xy′
2xcos(x^2+y)-y=xy′-y′ cos(x^2+ y)
2xcos(x^2+y)-y=y′(x-cos(x^2+ y))
y′={2xcos(x^2+y)-y}/(x-cos(x^2+ y))
则dy\dx= y′={2xcos(x^2+y)-y}/(x-cos(x^2+ y))
设函数y=f(x)由方程sin(x^2+y)=xy 确定,求dy\dx
设函数y=f(x)由方程sin(xy)+e^(x+y)=0确定,求dy/dx
设函数y=f(x),由方程xy-sin(x+y)=0,确定dy/dx
设y=y(x)由方程x^2-sin(xy)=2y确定,求dy/dx
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y=y(x)由方程e^xy+sin(xy)=y确定,求dy/dx.
设函数 y=y(x) 由方程y平方-2xy=7所确定 求 dy/dx
设由方程X-Y=e^(xy) 确定由函数Y=f(x),则dy/dx=?
设隐函数y=y(x)由方程x^y-e^y=sin(xy)所确定,求dy
设函数y=f(x)由方程e^xy -2x^2-y=3所确定.求dy/dx
设y=f(x) 由方程e^y=xy确定,则dy/dx=?
设函数y=f(x)由方程x+y=e^y确定,求dy/dx