设y=sin²[f(x²)],其中f具有二阶导数,求d²y/dx².

题目

设y=sin²[f(x²)],其中f具有二阶导数,求d²y/dx².

答案

设y=sin²[f(x²)],其中f具有二阶导数,求d²y/dx².
dy/dx=4sin[f(x²)]cos[f(x²)]f‘(x²)x
d²y/dx²=8{cos[f(x²)]}^2{f‘(x²)x}^2-8{sin(x²)]}^2{f‘(x²)x}^2+8sin[f(x²)]cos[f(x²)]f‘'(x²)x²+4sin[f(x²)]cos[f(x²)]f‘(x²)