求y=e^arctan(1/x)的导数

求y=e^arctan(1/x)的导数
求y=e^arctan(1/x)的导数

求y=e^arctan(1/x)的导数
须知(e^x)'=e^x,(arctanx)'=1/(1+x²)
y=e^arctan(1/x)
y'=e^arctan(1/x)·1/[1+(1/x)²]·(-1/x²)
=e^arctan(1/x)·x²/(1+x²)·(-1/x²)
=e^arctan(1/x)·-1/(1+x²)
=-e^arctan(1/x)/(1+x²)
=-e^arccot(x)/(1+x²)