隐函数求导x^2*y-6xy^3=-5RT

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隐函数求导x^2*y-6xy^3=-5RT
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隐函数求导x^2*y-6xy^3=-5RT
隐函数求导x^2*y-6xy^3=-5
RT

隐函数求导x^2*y-6xy^3=-5RT
x^2*y-6xy^3=-5
把5移到左边,得:
x^2*y-6xy^3+5=0
然后每项单独求导,得到
2xy+x^2y’-6y^3-18xy^2y’=0,
所以y’=(6y^3-2xy)/(x^2-18xy^2).

令f(x,y)=x^2*y-6xy^3+5
则fx=2xy-6y^3
fy=x^2-18xy^2
其中Fx,Fy是f(x,y)对x,y分别求导
f'= -Fx/Fy =(2xy-6y^3)/(18xy^2-x^2)

x^2*y-6xy^3=-5
两边对x求导:2xy+x^2y’-6y^3-18xy^2y’=0,
解出y’:y’=(6y^3-2xy)/(x^2-18xy^2).