Question

求方程所确定的隐函数y的导数dy/dx

Answer 1

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 + ylny

1 = (dy/dx)lnx + y/x + (dy/dx)lny + dy/dx

dy/dx = [1 - y/x]/[1 + ln(xy)] = y(x - y)/x(x + y)

2x²y - xy² + y³ = 0

4xy + 2x²dy/dx - y² - 2xydy/dx + 3y²dy/dx = 0

dy/dx = y(y - 4x)/(2x² - 2xy + 3y²)