设f(x)二阶可导,y=lnx*f(x^2)求二阶导数

问题描述:

设f(x)二阶可导,y=lnx*f(x^2)求二阶导数

一阶导数=lnx*f'(x^2)*2x+1/x*f(x^2)二阶导数=lnx*[f'(x^2)*2x]'+1/x*f'(x^2)*2x-1/x^2*f(x^2)+1/x*f'(x^2)*2x=lnx*[f'(x^2)*2+f''(x^2)*2x*2x]+1/x*f'(x^2)*2x-1/x^2*f(x^2)+1/x*f'(x^2)*2x