Question

设y=y(x)满足y'(x)=2e^x,求它的反函数的二阶导数. 谢谢,详细些,

Answer 1

y'(x)=2e^x

y=∫2e^xdx

y=2e^x+C=2e^(Cx)

Cx=ln(y/2)

x=Cln(y/2)=Clny-Cln2

x'=C/y

x''=-C/y^2