Question

y=arctanx的导数

y=arctanx的导数

Answer 1

看 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

Answer 2

x=tany 

y= arctanx 

dx/dy =1/sec^2(y)=1/(1+tan^2(y))=1/(1+x^2)

y'(x)=1/1+x^2

扩展资料：

三角函数求导公式：

(arcsinx)'=1/(1-x^2)^1/2

(arccosx)'=-1/(1-x^2)^1/2

(arctanx)'=1/(1+x^2)

(arccotx)'=-1/(1+x^2)

(arcsecx)'=1/(|x|(x^2-1)^1/2)

(arccscx)'=-1/(|x|(x^2-1)^1/2)

Answer 3

(arctanx)'=1/(1+x^2)

Answer 4

1/(1+x²)+C