求方程所确定的隐函数y的导数dy/dx
问题描述：
求方程所确定的隐函数y的导数dy/dx
x/y=In(xy)
2x^2y-xy^2+y^3=0
答
1、商的求导换成积的求导；2、对积的对数求导,改成对数的和求导.x = yln(xy) = ylnx + ylny1 = (dy/dx)lnx + y/x + (dy/dx)lny + dy/dxdy/dx = [1 - y/x]/[1 + ln(xy)] = y(x - y)/x(x + y)2x²y - xy² + y...