Question

设f(u)可导,y=f(secx^2),dy/dx为多少

Answer 1

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)