Find d²y/dx² if 4x²−2y²= 9

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/15 15:11:54

d(4x²−2y²)/dx = 0
8x - 4y*dy/dx = 0
dy/dx = 2x/y
d²y/dx² = d(dy/dx)/dx = d(2x/y)dx = [d(2x)dx*y - 2x*dy/dx]/y²
= [2y - 2x(2x/y)]/y²
= 2(y² - 2x²)/y³
再问：不好意思，d²y/dx² = d(dy/dx)/dx = d(2x/y)dx = [d(2x)dx*y - 2x*dy/dx]/y²这步有点不理解，是专门的公式？还是~，谢谢了
再答：干脆用另一种写法：两边对x求导: (4x²−2y²)' = 9' 8x - 4yy' = 0 y' = 2x/y 两边对x求导: y'' = [(2x)'*y - 2x*y']/y² (套用(uv)' = (u'v - uv')/v²) = (2y - 2xy')/y² = (2y - 2x*2x/y)/y² (代入y' = 2x/y) = 2(y² - 2x²)/y³ d²y/dx² = y'' = (y² - 2x²)/y³

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