Question

求隐函数的导数

求隐函数的导数第五题

Answer 1

两边取对数，
ylnx=xlny，然后求导
y'lnx+y/x=lny+xy'/y
整理得y'=(lny-y/x)/(lnx-x/y)

Answer 2

• x^y=y^x

  ylnx=xlny

  y'lnx+y/x=lny+x·y'/y

  y'(xylnx-x²)=xylny-y²

  y'=(xylny-y²)/(xylnx-x²)