xy∧2+lny+sin(3x+2y)=1确定y=y(x),求dy⼀dx

xy∧2+lny+sin(3x+2y)=1确定y=y(x),求dy/dx
2024-12-15 09:32:49
推荐回答(2个)
回答1:

xy∧2+lny+sin(3x+2y)=1
等式两边对x求导,
y^2+2xy*(dy/dx)+(dy/dx)/y+cos(3x+2y)(3+2(dy/dx))=0
(2xy+1/y+2cos(3x+2y))(dy/dx)=-y^2-3cos(3x+2y)
dy/dx=(-y^2-3cos(3x+2y))/((2xy+1/y+2cos(3x+2y))

回答2:

y^2+2xyy'+y'/y+cos(3x+2y)(3+2y')=0
y'=-[y^3+3ycos(3x+2y)]/[2xy^2+2ycos(3x+2y)+1]
dy/dx=-[y^3+3ycos(3x+2y)]/[2xy^2+2ycos(3x+2y)+1]