x^2+y^2-e^(arctan（y/x）)=0
2x+2y*y'-(arctan（y/x）)'e^(arctan（y/x）)=0
2x+2y*y'-1/(1+y^2/x^2)*(y'x-y)/x^2 *e^(arctan（y/x）)=0
2x+2y*y'-(y'x-y)/(x^2+y^2)*e^(arctan（y/x）)=0
2x+2y*y'-y'x/(x^2+y^2)*e^(arctan（y/x）)+y/(x^2+y^2)*e^(arctan（y/x）)=0
y'=(2x++y/(x^2+y^2)*e^(arctan（y/x）))/(x/(x^2+y^2)*e^(arctan（y/x）)-2y)这好像可以化为最简吧(2x+y)/(x-2y)
x^2+y^2=e^(arctan（y/x）),求dy/dx
x^2+y^2=e^(arctan（y/x）),求dy/dx
令F(x,y)=x^2+y^2-e^arctan(y/x)=0
对x求偏导 Fx = 2x-e^arctan(y/x) * 1/[1+(y/x)^2] * [-y/(x^2)]=2x + y/(x^2+y^2) * e^arctan(y/x)
然后e^arctan(y/x)用题目中的x^2+y^2代替 就可以把
即Fx=2x+y
对y求偏导 Fy=2y-e^arctan(y/x)*1/[1+(y/x)^2]*(1/x)=2y-x/(x^2+y^2) * e^arctan(y/x)
同上把e^arctan(y/x)用题目中的x^2+y^2代替 得 Fy=2y-x
∴ dy/dx= - Fx/Fy= - (2x+y) / (2y-x) = (2x+y)/(x-2y)
令F(x,y)=x^2+y^2-e^arctan(y/x)=0
对x求偏导 Fx = 2x-e^arctan(y/x) * 1/[1+(y/x)^2] * [-y/(x^2)]=2x + y/(x^2+y^2) * e^arctan(y/x)
然后e^arctan(y/x)用题目中的x^2+y^2代替 就可以把
即Fx=2x+y
对y求偏导 Fy=2y-e^arctan(y/x)*1/[1+(y/x)^2]*(1/x)=2y-x/(x^2+y^2) * e^arctan(y/x)
同上把e^arctan(y/x)用题目中的x^2+y^2代替 得 Fy=2y-x
∴ dy/dx= - Fx/Fy= - (2x+y) / (2y-x) = (2x+y)/(x-2y)
数学人气：493 ℃时间：2019-10-11 04:01:40
优质解答
我来回答
类似推荐
猜你喜欢
- 1已知多项多项式2x3-4x2-1除以多项式A得商式为2x，余式为x-1，则多项式A为_．
- 2一道英语题“This is one of the best films__________this year"
- 3作文写我的哥哥应该用哪句名言开头
- 4求自由落体的电梯中的水流出的速度
- 5The young man was happy that he saved the old woman(改为同义句)
- 6求lim(x趋向于3时)sin（x-3）/(x的平方减9)
- 7若关于x的方程x2+2x+k-1=0的一个根是0，则k=_．
- 8你想要一些水吗?Would you like some water句中的some可完成any吗?
- 9质量为m的物体随水平传送带一起匀速运动,A为传送带的终端皮带轮,皮带轮半径为r,要使物体通过终端时能水平抛出,皮带轮的转速至少为多少?
- 10英语单词记忆,有哪些方法?3Q