Question

arccot x和arccsc x这两个函数是否可导?

Answer 1

当然可导.y=arccot xx=cot y两边对x求导,得1=-y`csc^2 y=-y`(1+x^2)y`=-1/(1+x^2)y=arccsc xx=csc y1=-y`csc ycot y=-y`x√(csc^2 y-1)=-y`x√(x^2-1)(当x>0时)=y`x√(csc^2 y-1)=y`x√(x^2-1)(当x