Question

求y=arctanx的导数

Answer 1

y=arctanx,则x=tany
arctanx′=1／tany′
tany′=(siny/cosy)′=cosycosy-siny(-siny)/cos²y=1/cos²y
则arctanx′=cos²y=cos²y/sin²y+cos²y=1/1+tan²y=1/1+x²
故最终答案是1/1+x²
希望能帮到你

Answer 2

y=arctanx,所以tany=x 此时等式两边都求导
得y’tany’=1 则y’=1/tany’ 因y’=arctanx’
所以arctanx’ =1/tany’
而tany’=(siny/cosy)’=(siny’cosy-sinycosy’)/cosy的平方=(cosy的平方+siny的平方)/cosy的平方=1+tany的平方=1+x的平方
最终y’=1/1+x的平方

Answer 3

y=arctanx,则x=tany
arctanx′=1／tany′
tany′=(siny/cosy)′=cosycosy-siny(-siny)/cos²y=1/cos²y
则arctanx′=cos²y=cos²y/sin²y+cos²y=1/1+tan²y=1/1+x²
故最终答案是1/1+x²

Answer 4

x=tany
对x求导
1=y'*sec^2y
=>y'=1/sec^2y=1/(tan^2y+1)=1/(x^2+1）