Question

求隐函数导数,y的x次幂=x的y次幂

Answer 1

两边取对数

xlny=ylnx

两边对x求导

lny+xy'/y=y/x+y'lnx

两边乘以xy

xylny+y'x^2=y^2+y'xylnx

移项

y'x^2-y'xylnx=y^2-xylny

提取公因式

y'（x^2-xylnx）=y^2-xylny

y'=(y^2-xylny)/(x^2-xylnx)

用含有y的式子表达y的导数