设f(u)可导,y=f(secx^2),dy/dx为多少

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设f(u)可导,y=f(secx^2),dy/dx为多少

设f(u)可导,y=f(secx^2),dy/dx为多少
设f(u)可导,y=f(secx^2),dy/dx为多少

设f(u)可导,y=f(secx^2),dy/dx为多少
如果题目是secx²
令u=secx²,于是y=f(u),利用复合函数求导可知
dy/dx=(dy/du)*(du/dx)
=f'(u)*2x* secx² * tanx²
=2x* secx² * tanx² * f'(secx²)
如果题目是sec²x
令u=sec²x,于是y=f(u),利用复合函数求导可知
dy/dx=(dy/du)*(du/dx)
=f'(u)*2* sec²x* tanx
=2* secx² * tanx * f'(sec²x)

dx/dy=2xsecx^2tanx^2